If the nuclear radius of ²⁷Al is 3.6 fermi, the approximate nuclear radius of ⁶⁴Cu in fermi is

Solution

The half life of a radioactive nucleus is 50 days. The time interval (t₂– t₁) between the time t₂ when ²⁄₃ of it has decayed and the time t₁ when ¹⁄₃ of it had decayed is

30 days
50 days
60 days
15 days

Solution

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0, number of P species are 4 N₀ and that of Q are N₀. Half-life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be

3N₀
\(\frac{9N_{0}}{2}\)
\(\frac{5N_{0}}{2}\)
2N₀

Solution

A radioactive nucleus of mass M emits a photon of frequency v and the nucleus recoils. The recoil energy will be

Mc₂– hv
h²v²/ 2Mc²
zero
hv

Solution

The half life of a radioactive isotope ‘X’is 50 years. It decays to another element ‘Y’ which is stable. The two elements ‘X’and ‘Y’ were found to be in the ratio of 1 : 15 in as ample of a given rock. The age of the rock was estimated to be

150 years
200 years
250 years
100 years

Solution

The activity of a radioactive sample is measured as N₀ counts per minute at t= 0 and N₀/e counts per minute at t= 5 minutes. The time (in minutes) at which the activity reduces to half its value is

log_e2/5
\(\frac{5}{log_{e}2}\)
5 log₁₀2
5 log_e2

Solution

The mass of a \(_{3}^{7}\)Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucle on of \(_{3}^{7}\)Li nucleus is nearly

46 MeV
5.6 MeV
3.9 MeV
23 MeV

Solution

M_p denotes the mass of a proton and M_n that of a neutron.A given nucleus, of binding energy B, contains Z protons and N neutrons. The mass M(N, Z) of the nucleus is given by (c is the velocity of light)

M(N, Z) = NM_n + ZM_p + B/c²
M(N, Z) = NM_n + ZM_p – Bc²
M(N, Z) = NM_n + ZM_p + Bc²
M(N, Z) = NM_n + ZM_p – B/c²

Solution

Half lives of two radio active substance A & B are respectively 20 minutes & 40 minutes. Initially the samples of A & B have equal numbers of nulcei. After 80 minutes the ratio of remaining numbers of A& B nuclei is

1 : 16
4 : 1
1 : 4
1 : 1

Solution

In a fission reaction

\(_{92}^{26}U\rightarrow ^{177}X+^{177}Y+n+n\)

the binding energy per nucleon of X & Y is 8.5 MeV. Whereas of ²³⁶U is 7.6 MeV. The total energy liberated will be about

2000 MeV
200 MeV
2 MwV
200 KeV

Solution

Liberated energy Q = 117 × 8.5 + 117 × 8.5 – 236 × 7.6 =200 MeV. Thus, in fission of one Uranium nuclei nearly 200 MeV energy is liberated.

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