Radioactivity Questions and Answers

The mass defect in a nuclear fusion reaction is 0 05 What amount of energy will be librated in one kg fusion reaction 1 45 102 J 2 45 10 2 eV 3 45 10 J 4 45 10 2 KJ x

A human body excretes certain material by a law similar to radioactivity The body excretes half the amount injected in 24 h Find the time in which activity falls to 3uCi in hours if a person is injected technetium t 2 6h and its activity just after the injection is 6uCi Two conducting sphere of radius R are placed at a large distance from each other They are

28 The mean lives of a radioactive substances are 2000 years and 400 years for a and emission respectively What will be the time in years after which 5 6th of the given sample will decay if it is decaying by both a and B emission together In 6 1 79 1 297 2 397 3 597

Aakash Rank Booster Test Series for NEET 2020 43 The activity of a sample of a radioactive material is A at time t and A at time t t t If its mean life is T then 1 A t A t 3 A A e t t T 2 A A 1 t 4 A A e t t T

A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute After 5 minutes the rate is 1250 disintegrations per minute Then the decay constant per minute is 1 0 8 En 2 2 0 4 n 2 3 0 2 n 2 4 0 1 En 2

Consider the following nuclear reactions and select the correct statements from the options that follow Reaction 1 n p e Reaction II p n e v A Free neutron has higher mass than proton therefore reaction I is possible B Free proton has less mass than neutron therefore reaction II is not possible for the free proton C Inside a nucleus both decays reaction I and II are possible D Inside a nucleus reaction is not possible but reaction II is possible

ns 1 Activity of a sample is A at time t If it s activity is at time t then find the average life 5 t t n5 1 1 A Ao et A 2 Ae 5 en 5 t 1 t t n5 2 Radio active decay law n5 t t 3 n5 t t 4 t t ble

An atomic power nuclear reactor can deliver 300MW The energy released due to fission of each nucleus of uranium atom U238 is 170 MeV The number of uranium atoms fissioned per hour will be 1 30 x 10 5 3 10 x 102 2 4 1022 4 5 x 10 5

ect band gap semiconductor 16 op Hence correct option is d If relative density of tungeston is 18 8 gm cm and its atomic weight is 184 assuming that at room temperature there are two free electrons per atom calculate the density of free electrons n Soln Let volume 1 cm G

SolveLancer Test A radioactive medicine is to be given to a plant at 8 30 AM A solution of this was prepared at 6 40AM and 10 mL of this solution was to injected The scientist got stuck in traffic and arrived at office at 9 25 AM How much does should be given to plant t 1 hr 50 min SolveLancer Test a 10 mL b 20 mL c 14 1 mL d 7 07 mL CO a D b

Which of the following statements is false The energy spectrum of a decay is line spectrum The energy spectrum of B particles is continuous The energy spectrum of y decay is continuous The energy spectra of a y decay are line spectra

ARGER ENDEAVOUR A photo conductive cell 1 1mm CdS crystal is illuminated with light of wavelength 450 nm and intensity 1 mw cm Assuming quantum efficiency of unity Calculate the number of electron hole pairs generated per second given the energy band gap of CdS is 2 6 eV

The half life of a radioactive substance is 20 minutes The approximate time interval 1 1 between the time t when 2 3 of it has decayed and time t when 1 3 of it has decayed is a 7 min c 20 min b 14 min d 28 min

The rate of disintegration of a radioactive sample is P at time ty and R at time to The half life of the sample is proportional to Only one correct answer A P C D titty In R R t t In Ry In R In R R tx In R In R

9 The count rate for a radioactive source was found to be 1600 count sec At t 0 and t 8 sec this rate was 100 count sec What was the count rate at t 6 in counts sec 1 4000 3 200 2 300 4 150

If the mass of a hydrogen atom is 1 0078 u and that of a neutron is 1 0087 u then the binding energy of 12C is very nearly equal to 6 lu 931 MeV Ignore binding energy of the hydrogen atom A 920 MeV B 92 MeV C 9 2 MeV D 9200 MeV

Unstable radioactive nuclei of A are being formed at the rate of r atoms per second which have a disintegration constant of per second At t 0 there were no elements of A 1 A unstable At radioactive equilibrium for A the number of elements of A is found to be No Hence the average life of A is 1 2 3 Both 1 and 2 B stable 2 2 2 4 N

If 1 000 g of 226Ra refer to notation shown produces 0 0001 mL of the gas 222Rn refer to notation shown at STP standard temperature and pressure in 24h what is the half life of 226Ra in years Answer i e 1 x 10 or 1 x 10 2 226 P Da 222 Rn

16 4 2Q Assume that lamp radiates power P uniformly in 43 all directions The magnitude of electric field strength at a distance r from the lamp is P P 1 2 2ncer 3 P 3 4 2Q 1 stionpaper P CEOT P 2 P fayda P 2nceor

15 The activity of a radioactive substance is R at time t and R at time t t Its decay constant is A Then 1 R R 1 1 3 R t constant 2 R R e 2 4 R R e 4 1

14 A radioactive sample decays with decay constant A A capacitor of capacitance C is charged to some potential and then the plates are connected through a resistance R The value of R such that the ratio of the charge on the capacitor to the activity of the radioactive sample remains constant in time 1 3 2 1 2 ALIC

7 A certain radioactive material can undergo two different types of decay each with a different decay constant and 22 Then the effective decay constant is 1 2 3 6 2 37 4 4

16 A radioactive nucleus Po210 decays to a stable nucleus Pb206 Then time graph of rate of formation R of Pb206 against time t is best shown by R R 1 h 1 2 4 L I 3 R R Telegram ne

Photoemission by Black Body Radiation A black body emits peak spectral intensity at 9000 On increasing its temperature total radiation power increases by 81 times At the initial temperature when peak radiation of black body is allowed to fall on a metal surface assume other radiation are blocked by a filter it does not cause any photoemission but after increasing temperature the peak radiation of black body causes electrons come out which are stopped by a potential equal to the excitation energy of H atoms for n 2 to n 3 Bohr level Find work function of metal

Multiple Isotopes in a Radioactive Sample A sample of uranium is a mixture of three isotopes U234 U235 and U238 present in ratio of 0 006 0 71 and 99 284 respectively These have half lives 2 5 x 105 years 7 1 x 108 years and 4 5 x 10 years respectively Calculate the contribution to activity in of each isotope in sample

5 The wavelength of photon of energy E is same as moving with the 7 5 107 ms and kinetic energy the de Broglie wavelength of a material particle E E Then is

wooden cup from an site has an activity of 2 0 Bq The corresponding activity of newly cut wood is 8 4 Bq If the half life of 4C is 5730 years it can be concluded that the age of the cup is A less than 5730 years B between 5730 years and 11460 years C between 11460 years and 17190 years D greater than 17190 years An ancient archaeological

Two radioactive nuclei having half life periods 20 years and 15 years respectively have initial activities in the ratio 1 2 After how many years both posses equal activity 1 60 3 180 2 120 4 30

disintegration of a radioactive sample is R at time t and R at time t2 The half life of the sample is proportional to Only one correct answer A B C t t2 In R R t t In R In R t t D LD

There was initially 100mg of radioactive material After 6 hours its mass decreased by 3 If at any instance its disintegration is proportional to the quantity of material present determine how much is left after 24 hours

31 Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is ESC GH F CH M11547 7 3142 suit at waffech c div si a cuid di 1 9 31 2 5 27 3 3 23 4 7 29

A sample of radioactive element has a masss of 10 g at an instant t 0 The approximate mass of this element in the sample after two mean lives is a 2 50 g b 3 70 g c 6 30 g d 1 35 g

Calculate the minimum kinetic energy that the neutron should have in order to induce the reaction 0 6 n He C in which C is left in an excited state of energy 1 79 MeV Given Mass of 016 16 000000 simu NDEAVOUR Mass of n 1 008986 amu Mass of He4 4 003874 amu Mass of C13 13 007490 amu

Example 2 Boron naturally occurs as a mixtu of boron 10 5 protons 5 neutrons an boron 11 5 protons 6 neutrons isotope The percentage abundance of B 10 is 20 an that of B 11 is 80 Then the atomic mass boron is calculated as follows

A particle in the ground state of an infinitely deep one dimensional pot a perturbation of the form TIX V V cos a where is a constant Find the shift in energy of the particle in the lowest order perturbation theory

axes Two events 10 7 s apart in time take place at two points 50 m apart on the X axis Find the speed of an observer moving along the Xaxis who observes the two events simultaneously What will be the spatial separation between these two events as seen by this observer Consider a parallel plate air filled capacitor with a plate area of 10 cm separated by a distance of 2 mm

28 A radioactive nuclei with decay constant 0 5 s is being produced at a constant rate of 100 nuclei s If at t 0 there were no nuclei the time when there are 50 nuclei is a Is c In 2 s b 2 n 4 S d In 3 Intasambaul S

If a graph of Binding energy B A per nucleon versus mass number A looks like as shown in figure Then using the curve choose correct option s MeV B A 88 6 4 50 100 150 200 A Fusion of two nuclei with mass numbers 30 and 45 will have Q value of 99MeV Fission of nuclei with mass number 80 into two nuclei of equal mass number will have Q value of 256MeV Fission of nuclei with mass number 150 into two nuclei of equal mass number will release energy

A particle of mass M moving in a straight line with speed v collides with a stationary particle of the same mass In the center of mass coordinate system the first particle is deflected by 90 The speed of the second particle after collision in the laboratory system will be a v 2 b 2v c v d v 2

An infinitely long closely wound solenoid carries a sinusoidally varying current The induced electric field i a zero everywhere b non zero inside and zero outside the solenoid c non zero inside as well as outside the solenoid d zero inside and non zero outside the solenoid

Activity of a radioactive element 1 103 dps Its half life is 1 second After 3 second its activity will be dps decay per second 1 1000 dps 2 250 dps 4 None of these 3 125 dps

1 When the electron jumps from a level n 4 to n 1 the momentum of the recoiled hydrogen atom w be 4 n 1 affer recoiled 2 12 75 x 10 9 kg ms 4 zero 2 12 75 x 10 19 1 4 1 6 5 x 10 27 kg ms 3 13 6 x 10 19 kg ms 1 6 5 x 10 27 foll us 1 3 13 6 x 10 19 f us 1

The decay rate of sample of radioactive nuclide 1128 after time 4 min and 36 min is 322 and 161 cour s Find half life for this radionuclide fui f fa fa53 f 11284 min 36 min 322161 counts s 453 1 28 min f 334 2 32 min 3 16 min 4 40 min

3 Let L L L L denote the orbital angular momentum operators of a particle and let L L iL and L L iL The particle is in an eigenstate of L and L eigenvalues l l 1 and l respectively The expectation value of L L in this state is a l b 20h c 0 d l

The pure rotational levels of a molecule in the far infrared region follows the formula F J BJ J 1 where F J is the energy of the rotational level with quantum number J and B is the rotational constant The lowest rotational energy gap in rotational Raman spectrum is a 2B b 4B c 6B d 8B

N atoms of a radioactive element emits n alpha particles per second at an instant Then the half life of the element is sec 1 44

Plz explain each step and also tell why 3rd option is not orrect 142 Which of these is Q value of decay of Na into 10 Ne m m and m represent masses of Na atom Ne atom and electron respectively 1 m m c 2 m m 2m c

Radioisotopes are used an variety to manufacturing and testing techniques Wear measurements can be made using the following method An automobile engine is produced using piston ring with a total mass of 108g that includes 8 4 x 105 Bq of Fe whose half life is 45 days The engine is test run for 45 days after which the oil is drained and its activity is measured If the activity of the engine oil is 84 decays s How much mass was lost in 10 gm hr from the piston rings per hour of operation

Q 1 The decay of a population by catastrophic two body collision is described by the following differential equation dN dt KN Solve the given differential using ordinary differential equation integrated package in python Choose the initial condition N 500 and time points from 0 to 10

If 80 of a first order reaction was completed in E minutes then 50 of the same reaction would be completed in log 5 0 7 log 3 0 48 O 40 minutes O 70 minutes O 64 5 minutes O 34 4 minutes