The energy relation for the photoelectric effect is:
\[ eV_s = h\nu - \phi \]
where $eV_s$ is the stopping potential energy, $h\nu$ is the energy of incident photons, and $\phi$ is the work function.
Given: $h\nu = 2.48 \, \text{eV}, \, V_s = 0.5 \, \text{V}.$
\[ 0.5 = 2.48 - \phi \]
\[ \phi = 2.48 - 0.5 = 1.98 \, \text{eV}. \]
The work function of the material is $\phi = 1.98 \, \text{eV}.$
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to:
For the thermal decomposition of \( N_2O_5(g) \) at constant volume, the following table can be formed, for the reaction mentioned below: \[ 2 N_2O_5(g) \rightarrow 2 N_2O_4(g) + O_2(g) \] Given: Rate constant for the reaction is \( 4.606 \times 10^{-2} \text{ s}^{-1} \).