﻿ A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by | Nuclei

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# Nuclei

#### Multiple Choice Questions

21.

The half life of a radioactive substance is 20 minutes. The approximate time interval (t2 - t1) between the time t2 when 2/3 of it has decayed and time t1 when 1/3 of it had decayed is

• 14 min

• 20 min

• 28 min

• 7 min

B.

20 min

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# 22.A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by t = T log (1.3)

D.

At time t

also let initially there are total N0 number of nuclei
NA + NB = N0
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23.

Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be:

• 1: 16

• 4 : 1

• 1: 4

• 5: 4

D.

5: 4

Given 80 min = 4 half-lives of A = 2 half-lives of B.
Let the initial number of nuclei in each sample be N.

NA after 80 min = N/24

⇒ Number of A nuclides decayed  =

NB after 80 min  = N/22
⇒ Number of B nuclides decayed
therefore, the ratio of decayed numbers of A and B nuclei will be

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24.

Proton, Deuteron and alpha particle of the same kinetic energy is moving in circular trajectories in a constant magnetic field. The radii of the proton, deuteron and alpha particle are respectively rp, rd and rα. Which one of the following relations is correct?

•  rα = rp= rd

•  rα = rp< rd

•  rα > rd> rp

•  rα = rd> rp

B.

rα = rp< rd

For charged particle moving with a speed v, in magnetic field B, on a circular track of radius

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25.

Assume that a neutron breaks into a proton and an electron. The energy released during this process is(Mass of neutron = 1.6725 x 10–27kg; mass of proton = 1.6725 x 10–27kg; mass of electron = 9 x 10–31kg)

• 0.73 MeV

• 7.10 MeV

• 6.30 MeV

• 5.4 MeV

A.

0.73 MeV

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26.

A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α–particles and 2 positions. The ratio of number of neutrons to that of protons in the final nucleus will be

B.

In positive beta decay a, proton is transformed into a neutron and a positron is emitted

p+ → n0 + e+
Number of neutrons initially was A-Z
Number of neutrons after decay (A-Z) -3 x 2  (due to alpha particles) + 2 x 1 (due to positive beta decay)
The number of protons will reduce by 8. so, the ratio number of neutrons to that of protons =

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