The photograph below was taken by the James Webb Space Telescope (JWST) and shows a group of galaxies that formed shortly after the big bang, about $13 imes 10^9$ years ago - Edexcel - A-Level Physics - Question 15 - 2023 - Paper 2

One assumption is that the expansion of the universe has been uniform, meaning the rate of expansion (Hubble's constant) has remained constant over time.

Using the relation between parsecs and kilometers:

1 Mpc = $3.1 imes 10^{16}$ m = $3.24 imes 10^6$ light years.

To convert Hubble's constant from km/s/Mpc to SI units:

$H_0 = \frac{(60 \text{ to } 80) \text{ km/s}}{3.1 \times 10^{16} \text{ m}}$

This calculation must be done to determine if the value obtained is within the accepted range of $60-80$ km/s/Mpc.

The wavelength detected from Maisie is given by the formula:

$\lambda_{emitted} = \lambda_{observed} \times (1 + z)$

Substituting the values:

$\lambda_{emitted} = 4.0 \times 10^{-6} \text{ m} \times (1 + 14) = 4.0 \times 10^{-6} \text{ m} \times 15 = 6.0 \times 10^{-5} \text{ m}$

Thus, the wavelength emitted is $6.0 \times 10^{-5}$ m.

The light emitted by Maisie is redshifted due to the high value of $z$. The expansion of the universe stretches the wavelength of the light, moving it from its original emitted frequency into the infrared region of the electromagnetic spectrum.

The work function of the detector is 0.30 eV. To assess whether it can detect the light from Maisie, we must calculate the energy of the photons from Maisie's emitted light:

Using:

$E = \frac{hc}{\lambda}$

where $h = 6.63 \times 10^{-34}$ J·s and $c = 3.0 \times 10^8$ m/s, we find the energy corresponding to the wavelength $6.0 \times 10^{-5}$ m:

$E = \frac{6.63 \times 10^{-34} \times 3.0 \times 10^8}{6.0 \times 10^{-5}} = 3.31 \times 10^{-19} \text{ J} = \frac{3.31 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 2.07 ext{ eV}$

Since 2.07 eV is greater than 0.30 eV, the detector can detect the light from Maisie.