Question 181:
easyThe half life of a radioactive nucleus is 50 days. The time interval $(t_2 – t_1)$ between the time $t_2$ when 2 / 3 of it has decayed and the time $t_1$ when 1 / 3 of it had decayed is:
(2012 Mains)
At $t_1$, fraction remaining is $1 - 1/3 = 2/3$. At $t_2$, fraction remaining is $1 - 2/3 = 1/3$. The ratio of remaining nuclei is $(1/3)/(2/3) = 1/2$. This represents exactly one half-life, which is 50 days.
Question 182:
easyA radioactive sample with a half life of 1 month has the label: ‘Activity = 2 micro curies on $1-8-1991$’. What would be its activity two months earlier?
(1988)
Going backward in time by two months corresponds to adding 2 half-lives to the activity. The activity was $2 \times 2^2 = 2 \times 4 = 8$ micro curies.
Question 183:
easyWhat happens to the mass number and atomic number of an element when it emits $\gamma$-radiation?
(2020-Covid)
Gamma radiation involves the emission of high-energy photons when a nucleus transitions from a higher energy state to a lower one. This process does not alter the number of protons or neutrons, so the mass number and atomic number remain unchanged.
Question 184:
easy$\alpha$-particle consists of :
(2019)
An $\alpha$-particle is identical to a helium-4 nucleus, which contains exactly 2 protons and 2 neutrons, with no electrons.
Question 185:
easyA nucleus $^{m}_{n}X$ emits one $\alpha$ particle and two $\beta^-$ particles. The resulting nucleus is:
(2011 Pre)
Emission of an $\alpha$ particle reduces mass number by 4 and atomic number by 2 (result: $^{m-4}_{n-2}X'$). Emission of two $\beta^-$ particles increases atomic number by 2 while leaving mass number unchanged (result: $^{m-4}_{n-2+2}Z = ^{m-4}_{n}Z$).
Question 186:
easyThe number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:
(2009)
For every $x$ alpha particles, the atomic number decreases by $2x$. For $2x$ beta particles, the atomic number increases by $2x$. The net change in atomic number Z is zero. Nuclei with the same atomic number are isotopes.
Question 187:
easyIn the nuclear decay given below: $^{A}_{Z}X \rightarrow ^{A}_{Z+1}Y \rightarrow ^{A-4}_{Z-1}B^* \rightarrow ^{A-4}_{Z-1}B$, the particles emitted in the sequence are:
(2009)
Step 1: Z increases by 1, A is constant -> $\beta$ emission. Step 2: Z decreases by 2, A decreases by 4 -> $\alpha$ emission. Step 3: Excited state ($B^*$) to ground state ($B$) with no change in Z or A -> $\gamma$ emission. The sequence is $\beta, \alpha, \gamma$.
Question 188:
easyThe half life of radium is about 1600 years. Out of 100 g of radium existing now, 25 g will remain undecayed after:
(2004)
The fraction remaining is $25/100 = 1/4 = (1/2)^2$. This means 2 half-lives have passed. The time elapsed is $2 \times 1600 = 3200$ years.
Question 189:
easyHalf life of radioactive element is 12.5 hour and its quantity is 256 gm. After how much time its quantity will remain 1 gm:
(2001)
The fraction remaining is $1/256 = (1/2)^8$, which corresponds to 8 half-lives. Total time $t = 8 \times T_{1/2} = 8 \times 12.5 = 100$ Hrs.
Question 190:
easyThe relation between $\lambda$ and $T_{1/2}$ as ($T_{1/2} \rightarrow$ half life):
(2000)
By definition of radioactive decay, $N = N_0 e^{-\lambda t}$. At half-life $t = T_{1/2}$, $N = N_0/2$. So, $1/2 = e^{-\lambda T_{1/2}}$, which gives $\ln(2) = \lambda T_{1/2}$. Thus, $T_{1/2} = \frac{\ln 2}{\lambda}$.