If the de Broglie wavelength of the electron in n^th Bohr orbit in a hydrogenic atom is equal to 1.5 $$\pi $$a₀ (a₀ is Bohr radius), then the value of n/z is -

What is the work function of the metal if the light of wavelength 4000$$\mathop A\limits^ \circ $$ generates photoelectrons of velocity 6 $$ \times $$ 10⁵ ms^–1 from it ?
(Mass of electron = 9 $$ \times $$ 10^–31 kg;
Velocity of light = 3 $$ \times $$ 10⁸ ms^$$-$$1
Plank's constant = 6.626 $$ \times $$ 10^–34 Js;
Charge of electron = 1.6 $$ \times $$10^–19 JeV^–1)

The de Broglie wavelength ($$\lambda $$) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [v₀ is threshold frequency] :

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this purpose?

[R_H = 1 $$ \times $$ 10⁵ cm^–1, h = 6.6 $$ \times $$ 10^–34 Js, c = 3 $$ \times $$ 10⁸ ms^–1]