If alpha particle, proton and electron move with the same momentum, then their respective de-Broglie wavelengths λ_α, λ_p, λ_e are related

• λ_α = λ_p = λ_e

• λ_α < λ_p < λ_e

• λ_α > λ_p > λ_e

• λ_p > λ_e > λ_α

The velocity of a moving galaxy is 300 kms^-1 and the apparent change in wavelength of a spectral line emitted from the galaxy is observed as 0.5 nm. Then, the actual wavelength of the spectral line is

• 3000 $\stackrel{\circ }{\mathrm{A}}$

• 5000 $\stackrel{\circ }{\mathrm{A}}$

• 6000 $\stackrel{\circ }{\mathrm{A}}$

• 4500 $\stackrel{\circ }{\mathrm{A}}$

The temperature at which protons in proton gas would have enough energy to overcome Coulomb barrier of 4.14 x 10^-14 J is (Boltzmann constant = 1.38 x 10^-23 JK^-1)

• 2 × 10⁹ K

• 10⁹ K

• 6 × 10⁹ K

• 3 × 10⁹ K

The surface area ofa black body is 5 x 10^-4 m² and its temperature is 727°C. The energy radiated by it per minute is (σ = 5.67 × 10^-8 J/m² s-k⁴)

• 1.7 × 10³ J

• 2.5 × 10² J

• 8 × 10³ J

• 3 × 10⁴ J

The ratio of the de-Broglie wavelength of an α-particle and a proton of same kinetic energy is

• 1 : 2

• 1 : 1

• $1 : \sqrt{2}$

• 4 : 1

26.

A black body has maximum wavelength λ_m at 2000 K. Its corresponding wavelength at 3000 K will be

• $\frac{3}{2} {\mathrm{\lambda }}_{\mathrm{m}}$

• $\frac{2}{3} {\mathrm{\lambda }}_{\mathrm{m}}$

• $\frac{16}{81} {\mathrm{\lambda }}_{\mathrm{m}}$

• $\frac{81}{16} {\mathrm{\lambda }}_{\mathrm{m}}$

Band spectrum is also called

• molecular spectrum

• atomic spectrum

• flash spectrum

• line absorption spectrum

The ionization potential of hydrogen is 13.6 V. The energy required to remove an electron from the second orbit of hydrogen is

• 3.4 eV

• 6.8 eV

• 13.6 eV

• 1.51 eV

As the electron in Bohr orbit of hydrogen atom passes from state n = 2 to n= 1, the kinetic energy K and potential energy U change as

• K two-fold, U four-fold

• K four-fold, U two-fold

• K four-fold, U also four-fold

• K two-fold, U also two-fold

Let the potential energy of hydrogen atom in the ground state be regarded as zero. Then its potential energy in the first excited state will be

• 20.4 eV

• 13.6 eV 

• 10.2 eV

• 6.8 eV