If the nucleus  has a nuclear radius of about 3.6 fm, then  would have its radius approximately as: 

• 6.0 fm

• 9.6 fm

• 12.0 fm

• 12.0 fm

Two radioactive substance A and B have decay constants 5λ and λ respectively. At t = 0 they have the same number of nuclei. The ratio of a number of nuclei of A to those of B will be  after a time interval:

• 1/ 4λ

• 4λ

• 2λ

• 1/2λ

Monochromatic light of frequency 6.0 x 10¹⁴ Hz is produced by a laser. The power emitted is 2 x 10^-3 W The number of photons emitted, on the average, by the source per second is:

• 5 x 10¹⁵

• 5 x 10⁶

• 5 x 10¹⁷

• 5 x 10¹⁷

The binding energy of deuteron is 2.2 MeV and that of   is 28 MeV. If two deuterons are fused to form one  then the energy released is

• 25.8 MeV

• 23.6 MeV

• 19.2 MeV

• 19.2 MeV

In a radioactive material the activity at time t₁ is R₁ and at a later time t₂, it is R₂. If the dacay constant of the material is λ, then

• R₁ = R₂ e^{-λ(t₁ -t₂ )}

• R₁ = R₂ e^{λ(t₁ -t₂ )}

• R₁ = R₂ e(t₂ /t₁ )

• R₁ = R₂ e(t₂ /t₁ )

The radius of germanium (Ge) nuclide is measured to be twice the radius of  The number of nucleons in Ge are

• 73

• 74

• 75

• 75

Radioactive material 'A' has a decay constant '8λ' and material 'B' has decay constant 'λ'. Initially, they have a same number of nuclei. After what time, the ratio of a number of nuclei of material 'B' to that 'A' will be 1/e?

• 1/λ

• 1/7λ

• 1/8λ

• 1/8λ

For a radioactive material, the half-life is 10 minutes. If initially there are 600 number of nuclei, the time is taken (in minutes) for the disintegration of 450 nuclei is

• 20

• 10

• 15

• 30

When the radioactive isotope ${}_{88}\mathrm{R\alpha }^{226}$ decays in a series by the emission of three alpha (α) and a beta (β) particle, the isotope X which remains undecay is

• ${}_{83}\mathrm{X}^{214}$

• ${}_{83}\mathrm{X}^{218}$

• ${}_{83}\mathrm{X}^{220}$

• ${}_{83}\mathrm{X}^{223}$

N lamps each of resistance r, are fed by the machine of resistance R. If light emitted by any lamp is proportional to the square of the heat produced, prove that the most efficient way of arranging them is to place them in parallel arcs, each containing n lamps, where n is the integer nearest to.

• ${\left(\frac{\mathrm{r}}{\mathrm{NR}}\right)}^{3/2}$

• ${\left(\frac{\mathrm{NR}}{\mathrm{r}}\right)}^{1/2}$

• (NRr)^3/2

• (NRr)^1/2