The relation between λ and T_1/2 is:
(T_1/2 = half-life, λ → decay constant)

1. $T_{1/2}=\frac{\ln 2}{\lambda }$

2. $T_{1/2}$ $\ln 2=\lambda$

3. $T_{1/2}=\frac{1}{\lambda }$

4. $(\lambda +T_{1/2})=\frac{\ln }{2}$

If the half-life of a radionuclide is 77 days, then its decay constant is:
1.  0.003/day
2.  0.006/day
3.  0.009/day
4.  0.012/day

Which of the following are suitable for the fusion process?

The half-life of a sample of a radioactive element containing 4 × 10¹⁶ active nuclei, is 10 days. The number of decayed nuclei after 30 days will be: 

1. $0.5\times {10}^{16}$

2. $2\times {10}^{16}$

3. $3.5\times {10}^{16}$

4. $1\times {10}^{16}$

A sample of a radioactive element has a mass of 10 gm at an instant t = 0. The approximate mass of this element in the sample after two mean lives is:

1. 1.35 gm

2. 2.50 gm

3. 3.70 gm

4. 6.30 gm