Light of wavelength 180 nm ejects photoelectrons from a plate of metal whose work function is 2 eV. If a uniform magnetic field of 5 × 10^–5 Wb/m² is applied parallel to the plate, the radius of the path followed by the electrons ejected normally from the plate with maximum energy is

0.15 m

The correct answer is Option (1) → 0.15 m

$K_{\max }=\frac{h C}{\lambda}-\phi_0 \Rightarrow K_{\max }=\frac{12,400}{1800}-2$

$\Rightarrow K_{\max }=6.88-2=4.88 ~eV$

Also,  $r=\sqrt{\frac{2 m K . E}{q B}} \Rightarrow r \sqrt{\frac{2 \times m \times K . E}{q^2 B^2}}$

$\Rightarrow r=\sqrt{\frac{2 \times 9.1 \times 10^{-31} \times 4.88 \times 1.6 \times 10^{-19}}{1.6 \times 10^{-19} \times 1.6 \times 10^{-19} \times 25 \times 10^{-10}}}$

$\Rightarrow r=\sqrt{\frac{2 \times 9.1 \times 4.88}{1.6 \times 25} \times 10^{-2}}$

$=\sqrt{\frac{88.816}{40}} \times \frac{1}{10}=\frac{1.49}{10}=0.149 ~m \simeq 0.15 ~m$