Consider two radiations of wavelengths

1. $\lambda_1=2000\mathop {\rm{A}}\limits^{\rm{o}}$

2. $\lambda_2=6000 \mathop {\rm{A}}\limits^{\rm{o}}$

The ratio of the energies of these two radiations $\left(\frac{E_1}{E_2}\right)$ is $\_\_\_\_$ (Nearest integer).

The surface of sodium metal is irradiated with radiation of wavelength $x$ nm. The kinetic energy of ejected electrons is $2.8 \times 10^{-20}\ \text{J}$. The work function of sodium is $2.3$ eV. The value of $x$ is ________ $\times 10^2$ nm. (Nearest integer)

(Given: $h=6.6 \times 10^{-34}\ \text{J s}$ ; $1\ \text{eV} = 1.6 \times 10^{-19}\ \text{J}$ ; $c = 3.0 \times 10^8\ \text{m s}^{-1}$)

Two positively charged particles $m_1$ and $m_2$ have been accelerated across the same potential difference of 200 keV as shown below.

[Given mass of $m_1 = 1$ amu and $m_2 = 4$ amu]

The deBroglie wavelength of $m_1$ will be $x$ times of $m_2$. The value of $x$ is __________ (nearest integer)

The hydrogen spectrum consists of several spectral lines in Lyman series $\left(L_1, L_2\right.$, $\mathrm{L}_3 \ldots ; \mathrm{L}_1$ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series $\left(\mathrm{B}_1, \mathrm{~B}_2, \mathrm{~B}_3 \ldots ; \mathrm{B}_1\right.$ has lowest energy among Balmer lines). The energy of $L_1$ is $x$ times the energy of $B_1$. The value of $x$ is $\_\_\_\_$ $\times 10^{-1}$

. (Nearest integer)