\[ E = \phi + K_{\text{max}} \]
\[ \phi = \frac{hc}{\lambda_0} \]
\[ K_{\text{max}} = eV_0 \]
\[ 8e = \frac{hc}{\lambda} - \frac{hc}{\lambda_0} \quad \text{(i)} \]
\[ 2e = \frac{hc}{3\lambda} - \frac{hc}{\lambda_0} \quad \text{(ii)} \]
On solving (i) & (ii),
\[ \lambda_0 = 9\lambda \]
If the momentum of an electron is changed by P, then the de Broglie wavelength associated with it changes by \(1\%\). The initial momentum of the electron will be:
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32