Thank you for reporting, we will resolve it shortly
Q.
The K.E of the electron is E when the incident wavelength is $\lambda $ To increase the K.E of the electron to 2E, the incident wavelength must be
Dual Nature of Radiation and Matter
Solution:
Let Work function be $W$
According to Question,
$\frac{h c}{\lambda}-W=E $
$\Rightarrow W=\frac{h c}{\lambda}-E=\frac{h c-E \lambda}{\lambda}$
So,
Now, let the new $\lambda$ be $\lambda_{1}$, to get K.E. as $2 E$
So,
$\Rightarrow \frac{ hc }{\lambda_{1}}-\frac{ hc - E \lambda}{\lambda}=2 E$
$\Rightarrow \frac{ hc }{\lambda_{1}}=\frac{2 E \lambda+ hc - E \lambda}{\lambda}$
$\Rightarrow \frac{ hc \lambda}{ E \lambda+ hc }=\lambda_{1}$