Nuclei

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

Radioactive decay will occur as follows

$$\begin{gathered} {}_{86}{}^{220}\mathrm{Rn} \stackrel{ }{\to } {}_{84}{}^{216}\mathrm{PO} + {}_2{}^4\mathrm{He} \mathrm{Half} \mathrm{life} = 55\mathrm{s} \\ {}_{84}{}^{216}\mathrm{PO} \stackrel{ }{\to } {}_{82}{}^{212}\mathrm{Pb} + {}_2{}^4\mathrm{He} \mathrm{Half} \mathrm{life} = 0.66 \mathrm{s} \\ {}_{82}{}^{812}\mathrm{Pb} \stackrel{ }{\to } {}_{82}{}^{212}\mathrm{BL} + \mathrm{\lambda }°\mathrm{e} \mathrm{Half} \mathrm{life} = 10.6 \mathrm{h} \end{gathered}$$

If a certain mass of radon (Rn = 220) is allowed to decay in a certain container; then after 5 minutes the element with the greater mass will be

• radon

• polonium

• lead

• bismuth

A nucleus ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ has mass represented by m (A,Z). If m_p and m_n denote the mass of proton and neutron respectively and BE the binding energy (in MeV) then.

• $\mathrm{BE} = \left[\mathrm{m}\right(\mathrm{A},\mathrm{Z}) - {\mathrm{Zm}}_{\mathrm{p}} - (\mathrm{A}-\mathrm{Z}\left){\mathrm{m}}_{\mathrm{n}}\right]{\mathrm{C}}^2$

• $\mathrm{BE} = [{\mathrm{Zm}}_{\mathrm{p}} + (\mathrm{A} -\mathrm{Z}){\mathrm{m}}_{\mathrm{n}} - \mathrm{m}(\mathrm{A},\mathrm{Z}\left)\right]{\mathrm{c}}^2$

• $\mathrm{BE} = [{\mathrm{Zm}}_{\mathrm{p}} + {\mathrm{Am}}_{\mathrm{n}} - \mathrm{m} (\mathrm{A},\mathrm{Z}\left)\right]{\mathrm{c}}^2$

• $\mathrm{BE} = \mathrm{m} (\mathrm{A},\mathrm{Z}) - {\mathrm{Zm}}_{\mathrm{p}} - (\mathrm{A}-\mathrm{Z}) {\mathrm{m}}_{\mathrm{N}}$

The half-life period of a radioactive element X is the same as the mean life of another radioactive element Y. Initially, both of them have the same numbers of atoms then,

• X and Y have the same decay rate initially

• X and Y decay at the same rate always

• Y will decay at a faster rate than X

• X will decay at a faster rate than Y

The mass of a proton is 1847 times that of an electron. An electron and a proton are injected into a uniform electric field at right angle to the direction of the field with the same initial K.E.

• The electron trajectory will be less curved than the proton trajectory.

• both the trajectories will be straight

• the proton trajectory will be less curved than the electron trajectory.

• both the trajectories will be equally curved.