In a single slit diffraction experiment, for wavelength '$\lambda$', half angular width of the principal maxima is '$\theta$'. Also for wavelength of light '$p\lambda$', the half angular width of the principal maxima is '$q\theta$'. The ratio of the half angular widths of the first secondary maxima in the first case to second case will be

Photoelectric emission is observed from a metallic surface for frequencies $\nu_1$ and $\nu_2$ of the incident light rays ($\nu_1 > \nu_2$). If the ratio of maximum value of kinetic energy of the photoelectron emitted in first case to that in second case 3 : K, then the threshold frequency of the metallic surface is

The kinetic energy of a free electron increases to 3 times the previous K.E. The ratio of new de-Broglie wavelength to previous de-Broglie wavelength is

For wavelength of visible radiation of Hydrogen spectrum, Balmer gave an equation as $\lambda = \dfrac{xm^2}{m^2-4}$, where m is the integer value. The value of x in terms of Rydberg's constant R is