In the first excited state of hydrogen atom, the energy of its electron is -3.4 eV . The radial distance of the electron from the hydrogen nucleus in this case is approximately:

(Take $1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$ and $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 / \mathrm{C}^2$ )

A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12 . Keeping the box in stationary state over the trolley, the maximum acceleration with which the trolley can be moved horizontally in $\mathrm{m} \mathrm{s}^{-2}$ is:

$$ \left(g=10 \mathrm{~m} / \mathrm{s}^2\right) $$

Five capacitors of capacitances

$C_1=C_2=C_3=C_4=10 \mu \mathrm{~F}$ and $C_5=2.5 \mu \mathrm{~F}$ are connected as shown, along with a battery of 50 V .

The equivalent capacitance and the charges on each capacitor respectively are:

The amount of work done to raise a mass ' $m$ ' from the surface of the Earth to a height equal to the radius of the Earth ' $R$ ' will be