10.1 Define the term photoelectric effect - NSC Physical Sciences - Question 10 - 2022 - Paper 1

To find the number of photoelectrons emitted, we first determine the energy of one photon using the equation:

$E = hf$

Substituting the values:

• Planck's constant, $h = 6.63 imes 10^{-34} ext{ J s}$
• Frequency, $f = 1.2 imes 10^{15} ext{ Hz}$

Thus, the energy of one photon is:

$E = (6.63 imes 10^{-34} ext{ J s}) (1.2 imes 10^{15} ext{ Hz}) = 7.96 imes 10^{-19} ext{ J}$

Next, we calculate the number of photons emitted in one second by dividing the total energy (1.75 x 10^{5} J) by the energy per photon:

To find the maximum speed of the photoelectron, we can use the equation relating to the maximum kinetic energy:

$E_k = hf - W_0$

Where:

• $E_k$ is the kinetic energy of the photoelectron,
• $W_0$ is the work function (which can be expressed as $W_0 = hf_{threshold}$).

Calculate the work function: $W_0 = h f_{threshold} = (6.63 imes 10^{-34} ext{ J s})(9.09 imes 10^{14} ext{ Hz}) = 6.03 imes 10^{-19} ext{ J}$

Now, substituting back into the kinetic energy formula: $E_k = hf - W_0 = (6.63 imes 10^{-34} ext{ J s})(1.2 imes 10^{15} ext{ Hz}) - 6.03 imes 10^{-19} ext{ J}$

Calculating $E_k$ we get: $E_k = 7.96 imes 10^{-19} ext{ J} - 6.03 imes 10^{-19} ext{ J} = 1.93 imes 10^{-19} ext{ J}$

The maximum speed, $v_{max}$, can then be found from the kinetic energy formula:

$E_k = \frac{1}{2} mv^2$

Assuming the mass of the electron, $m = 9.11 imes 10^{-31} ext{ kg}$: $v_{max} = \sqrt{\frac{2E_k}{m}} = \sqrt{\frac{2(1.93 \times 10^{-19} \text{ J})}{9.11 \times 10^{-31} \text{ kg}}} = 1.93 \times 10^{6} \text{ m/s}$

An emission spectrum is formed when an atom in an excited state releases energy as it transitions to a lower energy state. As the electron moves to a lower energy level, it emits a photon of light with a specific wavelength corresponding to the difference in energy between the two states. The emitted light can be dispersed using a prism or diffraction grating, producing a spectrum that displays distinct lines. Each line corresponds to a specific transition between energy levels, revealing the unique electronic structure of the atom.