Physics NCERT Exemplar Solutions Class 12th Chapter Eleven

Relativistic corrections become necessary when the expression for the kinetic energy 1/2 mv², becomes comparable with mc². where m is the mass of the
At what de-Broglie wavelength, will relativistic corrections become important for an electron? 
(a) A=10nm (b) A =10^-1 nm (c) A=10^-4 nm (d) A=10^-6 nm

An electron mass m with initial velocity v=v₀i is an electric field E=E_o if $\lambda =\frac{h}{mv}=h/$ its debroglie wavelength at time t is given by

(a) ${\mathit{\lambda }}_{\mathit{o}}$

(b) ${\mathit{\lambda }}_{\mathit{o}}\sqrt[]{1+\frac{{\mathit{e}}^2{\mathit{E}}_{\mathit{o}}^2{\mathit{t}}^2}{{\mathit{m}}^2{\mathit{v}}_{\mathit{o}}^2}}$

(c) ${\mathit{\lambda }}_{\mathit{o}}/\mathit{}\sqrt[]{1+\frac{{\mathit{e}}^2{\mathit{E}}_{\mathit{o}}^2{\mathit{t}}^2}{{\mathit{m}}^2{\mathit{v}}_{\mathit{o}}^2}}$

(d) ${\mathit{\lambda }}_{\mathit{o}}/\mathit{}\sqrt[]{1+\frac{{\mathit{e}}^2{\mathit{E}}_{\mathit{o}}^2{\mathit{t}}^2}{{\mathit{m}}^2{\mathit{v}}_{\mathit{o}}^2}}$

An electron mass m with an initial velocity v=v_oi is in an electric field E=-E_oi. its debroglie wavelength at time t is given by $\mathrm{T}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}.$

(a) $\frac{{\mathit{\lambda }}_{\mathit{o}}}{1+\frac{\mathit{e}{\mathit{E}}_{\mathit{o}}}{\mathit{m}}\frac{\mathit{t}}{{\mathit{v}}_{\mathit{o}}}}$

(b) ${\mathit{\lambda }}_{\mathit{o}}\left(1+\frac{\mathit{e}{\mathit{E}}_{\mathit{o}}\mathit{t}}{\mathit{m}{\mathit{v}}_{\mathit{o}}}\right)$

(c) ${\mathit{\lambda }}_{\mathit{o}}$

(d) ${\mathit{\lambda }}_{\mathit{o}}\mathit{t}$

An electron is moving with an initial velocity v = v₀i and is in a magnetic field B = B₀ Then, its de-Broglie wavelength
(a) Remains constant
(b) Increases with time
(c) Decreases with time
(d) Increases and decreases periodically

A proton, a neutron, an electron and an a-particle have same energy. Then, their de-Broglie wavelengths compare as

(a) λp= λn > λe > λα     
(b) λα < p = n > λe
(c) λe< p = n> λα     
(d) λe = λp = λn = λα

Consider the figure given below. Suppose the voltage applied to A is increased. The diffracted beam will have the maximum at a value of θ that 

(a) Will be larger than the earlier value
(b) Will be the same as the earlier value
(c) Will be less than the earlier value
(d) Will depend on the target

Consider a beam of electrons (each electron with energy E₀) incident on a metal surface kept in an evacuated chamber. Then,
(a) No electrons will be emitted as only photons can emit electrons
(b) Electrons can be emitted but all with an energy, E₀
(c) Electrons can be emitted with any energy, with a maximum of E₀– ɸ (ɸ  is the work function)
(d) Electron can be omitted with energy ,with a maximum of E₀

The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly
(a) 1.2 nm
(b) 1.2 x 10-3 nm
(c) 1.2 x 10-6  nm
(d). 1.2 x 10 nm

A particle is dropped from a height H. The de-Broglie wavelength of the particle as a function of height is proportional to  (a) H  (b) H^1/2 (c) H⁰   (d) H^-1/2