10.1 Two small spheres, A and B, made of pure zinc are at rest 0.1 m apart on a wooden table - NSC Physical Sciences - Question 10 - 2023 - Paper 1

To determine whether the ultraviolet light will eject electrons from sphere B, we can use the equation for the energy of a photon: $E = hf$ where:

• $E$ is the energy of the photon,
• $h = 6.63 imes 10^{-34} ext{ J s}$ (Planck's constant),
• $f = 2.8 imes 10^{16} ext{ Hz}$ (frequency of light).

Calculating the energy: $E = (6.63 imes 10^{-34})(2.8 imes 10^{16}) = 1.86 imes 10^{-17} ext{ J}$

Comparing the photon energy with the work function of zinc ($W_0 = 6.63 imes 10^{-19} ext{ J}$): Since $1.86 imes 10^{-17} ext{ J} > 6.63 imes 10^{-19} ext{ J}$, the photon energy exceeds the work function, thus the ultraviolet light will eject electrons from sphere B.

To find the minimum number of photons needed, we must first find the charge required for sphere A to be moved: Using Coulomb's law: F = rac{kQ_1Q_2}{r^2} Here:

• $F = 0.027 ext{ N}$,
• $Q_1 = 5.4 imes 10^{-6} ext{ C}$ (charge on sphere A),
• $k = 8.99 imes 10^9 ext{ N m}^2/ ext{C}^2$.

Rearranging gives: Q_2 = rac{Fr^2}{kQ_1} Assuming $r = 0.1 ext{ m}$: Q_2 = rac{(0.027)(0.1)^2}{(8.99 imes 10^9)(5.4 imes 10^{-6})} = 5.56 imes 10^{-9} ext{ C}

Now we calculate the number of photons (n) by: n = rac{Q}{e} Where $e = 1.6 imes 10^{-19} ext{ C}$ (charge of an electron): n = rac{5.56 imes 10^{-9}}{1.6 imes 10^{-19}} \\ n = 3.47 imes 10^{10} ext{ photons} Hence, a minimum of $3.47 imes 10^{10}$ photons is required to move sphere A.

The type of line spectrum observed is called an absorption spectrum.

The absorption spectrum consists of a series of dark lines or bands superimposed on a continuous spectrum of colors. These dark lines correspond to specific wavelengths of light that have been absorbed by the cold gas, indicating the presence of certain elements which absorb those particular wavelengths.

Diagram A is the correct choice, as it indicates transitions that would produce the necessary energy levels corresponding to the absorption spectrum observed.