Question

Wavelengths belonging to Balmer series lying in the range of $450nm$ to $750nm$ were used to eject photoelectrons from a metal surface whose work function is $2.0eV$ . The maximum kinetic energy of the emitted photoelectrons is $a$ . Write value of $100a$ . (Take $hc=1242eVnm$ .)

Answer 1

Wavelengths corresponding to minimum wavelength (λ_min ) or maximum energy will emit photoelectrons having kinetic energy which is maximum. (λ_min) belonging to Balmer series and Lying in the given range (450 nm to 750 nm) corresponds to transition from (n = 4 to n = 2). Here,
$E_{4}=-\frac{1 3 . 6}{\left(4\right)^{2}}=-0.85\text{eV}$
$\left(\text{and} E\right)_{2}=-\frac{1 3 . 6}{\left(2\right)^{2}}=-3.4\text{eV}$
$\therefore \Delta E =E ⁡_{4}-E ⁡_{2}=2.55\text{eV}$
$K _{\text{max}}=\text{Energy of photon}-\text{work function}=2.55-2.0=0.55\text{eV=a}$
Hence, $100a=55$