A group of students investigates the relationship between the work function of different metals and the maximum kinetic energy of the ejected electrons when the metals are irradiated with light of suitable frequency - NSC Physical Sciences - Question 11 - 2018 - Paper 1

The dependent variable for this investigation is the maximum kinetic energy of the ejected electrons.

One control variable for this investigation could be the wavelength of the ultraviolet light used.

Based on the data provided, silver has the smallest maximum kinetic energy (9.19 x 10^18 J) among the metals listed. According to the photoelectric effect, a smaller kinetic energy indicates a larger work function, thus silver has the largest work function.

To calculate the work function of potassium, we can use the photoelectric equation:

h f = W_0 + rac{1}{2} mv^2

From the given data, we find:

• Maximum kinetic energy of potassium $Ek(max) = 9.58 imes 10^{18} J$
• Wavelength $\lambda = 2 imes 10^{-8} m$

We can first find the frequency using the equation:

$c = \lambda f$

where $c = 3.00 \times 10^8 \text{ m/s}$.

Rearranging gives:

$f = \frac{c}{\lambda} = \frac{3.00 \times 10^8}{2 \times 10^{-8}} = 1.5 \times 10^{16} Hz$

Now, substituting into the photoelectric equation:

$W_0 = h f - Ek(max)$

Using Planck's constant $h = 6.63 \times 10^{-34} J s$, we can calculate:

$W_0 = 6.63 \times 10^{-34} \times 1.5 \times 10^{16} - 9.58 \times 10^{18} = 9.945 \times 10^{-18} - 9.58 \times 10^{18} = 3.65 \times 10^{-19} J$

An increase in the intensity of the ultraviolet light increases the number of photons per second hitting the metal surface. This results in more electrons being ejected, which can lead to a higher maximum kinetic energy of the ejected electrons, assuming that the energy of the photons remains constant. Therefore, the answer is: INCREASES.