41.

de Broglie wavelength λ associated with neutrons is related with absolute temperature T as

• λ ∝ T

• λ ∝ $\frac{1}{\mathrm{T}}$

• λ ∝ $\frac{1}{\sqrt{\mathrm{T}}}$

• λ ∝  T²

A nucleus of mass number 220 decays by $\mathrm{\alpha }$ decay. The energy released in the reaction is 5 MeV. The kinetic energy of an $\mathrm{\alpha }$-particle is

• $\frac{1}{54}$MeV

• $\frac{27}{11}$ MeV

• $\frac{54}{11}$ MeV

• $\frac{55}{54}$ MeV

The wavelengths of K_α  X- rays for lead isotopes  Pb²⁰⁸ , Pb²⁰⁶  and  Pb²⁰⁴ are  λ₁, λ₂ and  λ₃ respectively. Then

• λ₂ = $\sqrt{{\mathrm{\lambda }}_1 {\mathrm{\lambda }}_3}$

• λ₂ = λ₁ + λ₃

• λ₂ = λ₁ λ₂

• λ₂ =  $\frac{{\mathrm{\lambda }}_1}{{\mathrm{\lambda }}_3}$

Light with an energy flux of 18 W/cm² falls on a non-reflecting surface at normal incidence. The pressure exerted on the surface is

• 2 N/m²

• 2 × 10^-4 N/m²

• 6 N/m²

• 6 × 10^-4 N/m²

The dimensional formula of Planck's constant is

• [ M L² T^-1 ]

• [ M L² T^-2 ]

• [ M L⁰ T² ]

• [ M L T² ]

Which out of the following, cannot produce two coherent sources?

• Lloyd's mirror

• Fresnel biprism

• Young's double slit

• Prism

In  Young's  double  slit experiment, the  two  slits  act  as coherent  sources  of  equal  amplitude  $\mathrm{\alpha }$  and  of  wavelength  λ. In  another  experiment  with  the  same  set  up,  the two  slits  are  sources  of  equal  amplitude  $\mathrm{\alpha }$  and  wavelength  λ, but  are  incoherent. The  ratio  of  intensities  of  light  at  the  midpoint  of  the  screen  in  the  first  case  to  that  in  the  second  case  is

• 2 : 1

• 1 : 2

• 3 : 4

• 4 : 3

If  the  kinetic  energy  of  a  particle  is  increased  by  16  times,  the  percentage  change  in  the  de Broglie  wavelength  of  the particle  is

• 25 %

• 75 %

• 60 %

• 50 %

If  the  half  lives  of  a  radioactive  element  for  $\mathrm{\alpha }$  and  β  decay  are  4  years  and  12  years  respectively,  the  ratio  of  its  initial  activity  and  that  after  12  years will be

• 6.25 %

• 12.5 %

• 25 %

• 50 %

In  the  given  circuit,  the  potential difference  between  A  and  B  is

• 0

• 5 volt

• 10 volt

• 15 volt