When a electron in hydrogen atom  falls to the ground state from n = 2 , 10.2 eV of energy is emitted. What is the wavelength of this radiation? (Note: 1 eV = $1.60 \times {10}^{-19}$J and h = $6.626 \times {10}^{-34}$J-s)

1.  $5.76 \times {10}^{-9}m$

2.  $1.22 \times {10}^{-7}m$

3.  $3.45 \times {10}^{-7}m$

4.  $2.5 \times {10}^{15}m$

Electrons of mass m with de- Broglie wavelength λ fall on the target in an X-ray tube. The cut off wavelength (λ_o) of the emitted X-ray is :

1.  ${\mathrm{\lambda }}_0=\frac{2{\mathrm{mc\lambda }}^2}{\mathrm{h}}$

2.  ${\mathrm{\lambda }}_0=\frac{2\mathrm{h}}{\mathrm{mc}}$

3.  ${\mathrm{\lambda }}_0=\frac{2{\mathrm{m}}^2{\mathrm{c}}^2{\mathrm{\lambda }}^2}{{\mathrm{h}}^2}$

4.  ${\mathrm{\lambda }}_0=\mathrm{\lambda }$

An electron of mass m with an initial velocity $\overrightarrow{v}={\mathrm{v}}_0\hat{i}({\mathrm{v}}_0>0)$enters in an electric field $\overrightarrow{\mathrm{E}}=-E_0\hat{i}$ (E_o = constant >0) at t = 0. If ${\mathrm{\lambda }}_0$, is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is:-

1. $\frac{{\mathrm{\lambda }}_0}{\left(1+{\displaystyle \frac{{\mathrm{eE}}_0}{{\mathrm{mv}}_0}}\mathrm{t}\right)}$

2. ${\mathrm{\lambda }}_0\left(1+\frac{{\mathrm{eE}}_0}{{\mathrm{mv}}_0}\mathrm{t}\right)$

3. ${\mathrm{\lambda }}_0\mathrm{t}$

4. ${\mathrm{\lambda }}_0$

When light of frequency 2$\nu$_o (where $\nu$_o is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is ${\mathrm{v}}_1$. When the frequency of the incident radiation is increased to 5$\nu$_o, the maximum velocity of electrons emitted from the same plate is ${\mathrm{v}}_2$. The ratio of ${\mathrm{v}}_1$ to ${\mathrm{v}}_2$ is

1. 1: 2

2. 1: 4

3. 4: 1

4. 2: 1

A photoelectric surface is illuminated successively by the monochromatic light of wavelength $\mathrm{\lambda }$ and $\frac{\mathrm{\lambda }}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface of the mineral is :
[h=Plank’s constant, c=speed of light]

1. $\frac{hc}{2\lambda }$

2. $\frac{hc}{\lambda }$

3. $\frac{2hc}{\lambda }$

4. $\frac{hc}{3\lambda }$

Light of wavelength 500 nm is incident on metal with work function 2.28 eV. The de-Broglie wavelength of the emitted electron is :

1. $<2.8\times {10}^{-10}m$

2. $<2.8\times {10}^{-9}m$

3. $\ge 2.8\times {10}^{-9}m$

4. $\le 2.8\times {10}^{-12}m$

Which of the following figures represent the variation of the particle momentum and the associated de-Broglie wavelength?

1. 

2. 

3. 

4.