Light of different frequencies is incident on a metal plate. The sketch graph below shows the relationship between the maximum kinetic energy, Ekm, of the photoelectrons and the energy of the incident photons.

$$E_{k,max} = E_{photon} - W_0$$

This equation is in the form $y = mx + c$, where $m$ is the gradient.

The numerical value of the gradient is $\boxed{\text{1}}$.

10.3
10.3.1

$E_{k,max} = \frac{1}{2}mv^2$. The mass of an electron ($m_e$) is $9.11 \times 10^{-31}$ kg.

$$2.99 \times 10^{-19} \text{ J} = \frac{1}{2} (9.11 \times 10^{-31} \text{ kg}) v^2$$

$$v^2 = \frac{2 \times 2.99 \times 10^{-19} \text{ J}}{9.11 \times 10^{-31} \text{ kg}}$$ $$v^2 = \frac{5.98 \times 10^{-19}}{9.11 \times 10^{-31}} \text{ m}^2/\text{s}^2$$ $$v^2 \approx 6.564 \times 10^{11} \text{ m}^2/\text{s}^2$$

$$v = \sqrt{6.564 \times 10^{11} \text{ m}^2/\text{s}^2}$$ $$v \approx \boxed{8.10 \times 10^5 \text{ m/s}}$$

10.3.2

Use the photoelectric equation: $E_{photon} = W_0 + E_{k,max}$.

$$Y = 3.66 \times 10^{-19} \text{ J} + 2.99 \times 10^{-19} \text{ J}$$

$$Y = (3.66 + 2.99) \times 10^{-19} \text{ J}$$ $$Y = \boxed{6.65 \times 10^{-19} \text{ J}}$$

10.4
The maximum kinetic energy of the photoelectrons will REMAIN THE SAME.

Reason: The maximum kinetic energy of photoelectrons depends only on the energy (or frequency) of the individual incident photons and the work function of the metal. It does not depend on the intensity (number of photons per second) of the incident light. Increasing the number of photons per second only increases the number of photoelectrons emitted, not their individual maximum kinetic energy.