Radioactive decay is the process in which an atom loses it’s energy because of emitting particles. There are three types of radioactive decay:-

1. Alpha Decay

2. Beta Deccay

3. Gamma Decay
Alpha decay occurs due to the present of too many protons in the nucleus which causes excessive repulsion. Beta deccay occurs when the ratio of neutron to proton is greater in the nucleus and causes instability. Gamma decay occurs when the nucleus is at high energy.

Worksheet questions

$_zA^A \to _{z-2}C^{A-4} \to _zA^{A-4}$

The sequence of radiation emitted is:

(a)    $\alpha, \beta, \gamma$

(b)   $\alpha, \beta, \beta$

(c)    $\beta, \alpha, \alpha$

(d)   $\alpha, \gamma, \gamma$

2. Out of a radioactive sample 90% is found after one day. What present of the original sample can be found after 2 days:

(a)    64%

(b)   72%

(c)    81%

(d)   45%

3. A radioactive isotope X with half life of $1.37 \times 10^9$ years decay to Y which is stable. A sample of rocks was found to contain both the elements X and Y in the mole ratio 1 : 7. what is the age of the rock

(a)    $1.96 \times 10^8 yrs$

(b)   $3.85 \times 10^9 yrs$

(c)    $4.11 \times 10^9 yrs$

(d)   $9.06 \times 10^6 yrs$

4. If 80% of a radioactive element undergoing decay is left over after a certain period of time t from the start, how many such periods should elapse from the start for eh 50% of the element to be left over:

(a)    4

(b)   6

(c)    5

(d)   3

5. Two radioactive elements A and B have half life lives in the ratio of 1 : 2. If half life of A is 2 days, what will be the mole ratio of A to B after 12 days in a sample initially containing 1 mole of each:

(a)    1 : 2

(b)   1 : 4

(c)    1 : 6

(d)   1 : 8

6. The fraction of a radioactive element that decays in time t, is given by $(\lambda = \text{decay constant)}$:

(a)    $\lambda^{-\lambda t}$

(b)   $1- e^{-\lambda t}$

(c)    $\dfrac{1}{e^{-\lambda t}}$

(d)   $\dfrac{1}{1- e^{-\lambda t}}$

7. Gamma ray emission during radioactive decay is due to the:

(a)    Fall of exited electron to the lower energy state

(b)   Return of exited nucleus, left over by $\alpha \text{and} \beta$-emission, into the lower energy state

(c)    Too large n / p ratio [To decrease it]

(d)   Too small n / p ratio [To increase it]

8. Two radioactive nuclides A and B have half life lives in the ratio 2 : 3 starting with a sample containing the two nuclides in equimolar amount, what would be the mole ratio $n_A : n_B$ after a time interval which is three times of the half life of A?

(a)    1 : 2

(b)   2 : 1

(c)    1 : 3

(d)   1 : 4

9. A radioactive sample has an initial activity of 64 dpm. 15 minutes later it has an activity of 32 dpm. what would be the number of atoms in a sample having an activity of 6.93 dpm:

(a)    300

(b)   150

(c)    450

(d)   200

10. Which of the following nuclides is positron emitter?

(a)    $_1H^3$

(b)   $_2He^6$

(c)    $_5B^{12}$

(d)   $_7N^{13}$

11. A radioactive isotope A decays into another isotope B which has half life equal to half of A. if a sample consists initially of atoms of A only, the net activity of the sample:

(a)    Increases with time

(b)   Decreases with time

(c)    Remains constant

(d)   None of these

12. A compound tagged with radioactive tritium, $_1H^3$ has an activity of $3.2 \times 10^8$ cpm. How much time would it take for the activity to decline to $2 \times 10^7 \text{cpm}$ $t_{1/2} \text{of} _1H^3 = 12.26 yrs$

(a)    24.52 yrs

(b)   36. 78 yrs

(c)    49.04 yrs

(d)   98.04 yrs

13. The half life of a radioactive element is 30 min. the time interval between the stages of 33.3% and 67.7% decay will be:

(a)    60 min

(b)   90 min

(c)    30 min

(d)   45 min

14. Elements with odd atomic numbers never have:

(a)    More than 2 stable isotopes

(b)   Moe than 3 stable isotopes

(c)    More than 6 stable isotopes

(d)   More than 4 stable isotopes

15. Which of the following is most likely to decay by $\beta^+$ emission?

(a)    $^{63}Cu$

(b)   $^{67}Cu$

(c)    $^{59}Cu$

(d)   $^{68}Cu$

16. Which has highest binding energy per nucleon:

(a)    $^2_1H$

(b)   $^{56}_{26}Fe$

(c)    $^{235}_{92}U$

(d)   $^{16}_8$

17. In the transformation of $^{238}_{92}U \text{to} ^{234}_{92}U$, if one emission is an $\alpha$-particle, what should be the other emission (s)?

(a)    One $\beta^- \text{and one} \gamma$

(b)   One $\beta^+ \text{and} \gamma^-$

(c)    Two $\gamma$

(d)   Two $\beta^- \text{and one} \beta^+$

1. (b)       2. (c)        3. (c)      4. (d)           5. (d)

6. (c)       7. (b)        8. (a)      9. (b)          10. (d)

11. (a)     12. (c)       13. (c)    14. (a)         15. (c)

16. (b)      17. (c)

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