A metal target with atomic number $Z=46$ is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio $r$ of the wavelengths of the $K_\alpha$-line and the cut-off is found to be $r=2$. If the same electron beam bombards another metal target with $Z=41$, the value of $r$ will be

A photoelectric material having work-function $${\phi _0}$$ is illuminated with light of wavelength $$\lambda \left( {\lambda < {{he} \over {{\phi _0}}}} \right).$$ The fastest photoelectron has a de-Broglic wavelength $${\lambda _d}.$$ A change in wavelength of the incident light by $$\Delta \lambda $$ result in a change $$\Delta {\lambda _d}$$ in $${\lambda _d}.$$ Then the ratio $$\Delta {\lambda _d}/\Delta \lambda $$ is proportional to

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength ($$\lambda $$) of incident light and the corresponding stopping potential (V₀) are given below:

$$\lambda \left( {\mu m} \right)$$	V0(Volt)
0.3	2.0
0.4	1.0
0.5	0.4

Given that c = 3 $$ \times $$ 10⁸ ms^-1 and e = 1.6 $$ \times $$ 10^-19 C, Planck's constant (in units of J-s) found from such an experiment is) :