Question

Read the following :
(i) The half-life period of a radioactive element X is same as the mean-life time of another radioactive element Y. Initially, both of them have the same number of atoms. Then Y will decay at a faster rate than X.
(ii) The electron emitted in beta radiation originated from the decay of a neutron in a nucleus.
(iii) The half-life of ${}^{215}$ A is 100 ms. The time taken for the radioactivity of a sample of ${}^{215}$ At to decay to $1/{16}^{th}$ of its initial value is 400 ms.
(iv) The volume (V) and mass (m) of a nucleus are related us $V\propto$ m.
(v) Given a sample of Radium - 226 has a half-life of 4 days. Then nucleus disintegrates 3/4 within 2 half-lives.
Select the correct code for above:

• A. TTTTT
• B. TFTTF
• C. FTFTF
• D. FTTTF

Answer 1

The correct option is A TTTTT

The average life period of a first order reaction is equal to the reciprocal of its rate constant.
Thus $\lambda =\frac{1}{k}$
The half life period is $t_{1/2}=\frac{0.693}{k}$
Thus the decay constant for x is 0.693 times the decay constant for y. Hence, Y will decay at a faster rate than X..
Thus statement (1) is true.
In the nucleus, a neutron loses an electron to form a proton. Thus, the electron emitted in beta radiation originated from decay of a neutron in a nucleus. hence, the statement (ii) is correct.
$A_0\stackrel{100ms}{\to }\frac{A_0}{2}\stackrel{100ms}{\to }\frac{A_0}{4}\stackrel{200ms}{\to }\frac{A_0}{4}\stackrel{300ms}{\to }\frac{A_0}{8}\stackrel{400ms}{\to }\frac{A_0}{168}$
Thus statement (iii) is correct.
More is the mass of the nucleus, more will b its volume. The volume ( V ) and mass (m) of a nucleus are related us V m. Hence, the statement (iv) is correct.