In the diffraction pattern, the first maximum is at $30^\circ$, when a monochromatic light of wavelength $\lambda$ is incident on a slit of width $a$. For the same wavelength, if the slit width is changed, so that first maximum is at $45^\circ$. The slit width is changed by $\left(\sin 30^\circ = \dfrac{1}{2}, \sin 45^\circ = \dfrac{1}{\sqrt{2}}\right)$

The ratio of de-Broglie wavelength of an $\alpha$-particle and proton accelerated from rest by the same potential is $\dfrac{1}{\sqrt{m}}$. The value of $m$ is

The kinetic energy of the electron in an orbit of radius $r$ in hydrogen atom is proportional to ($e$ = electronic charge)

Which of the following is an integral multiple of $\dfrac{h}{2\pi}$ in Bohr's model of an hydrogen atom?