Calculate the maximum kinetic energy of photoelectrons emitted from a metal plate when light of wavelength [tex]\lambda = 520 \, \text{nm}[/tex] is directed at the metal surface.
- Work function ([tex]\Phi[/tex]) of the plate = [tex]1.1 \times 10^{-19} \, \text{J}[/tex]
- Planck's constant ([tex]h[/tex]) = [tex]6.63 \times 10^{-34} \, \text{Js}[/tex]
- Frequency ([tex]f[/tex]) = [tex]\frac{c}{\lambda}[/tex]
- Speed of light in a vacuum ([tex]c[/tex]) = [tex]3.00 \times 10^{8} \, \text{ms}^{-1}[/tex]
- Maximum kinetic energy ([tex]E_{k\text{max}}[/tex]) = [tex]hf - \Phi[/tex]
Note: The wavelength must be converted to meters: [tex]\lambda = 520 \times 10^{-9} \, \text{m}[/tex]
Calculate the value to verify your results.
Answer (3)
Well for a start, 520nm is 520 nanometres and for some reason you've called it 590 x10^-9 (590 isn't standard form) where it's actually 5.2 ×10^-7 metres. Put that into the equations: f = c/λ = 3.0 x10^8/5.2 ×10^-7 = 5.77 x10^14 (3 s.f.) (5.77 x10^14) x (6.63 x10^-34) - (1.1 x10^-19) = 2.73 x10^-19 J
To calculate the maximum kinetic energy of photoelectrons emitted from a plate when light of wavelength 520 nm is directed at the metal surface, we will use the provided data:
Work function (Ф) of the plate = 1.1 × 10⁻¹⁹ J
Planck's constant (h) = 6.63 × 10⁻¹⁹ J.s
Speed of light in vacuum (c) = 3.00 × 10⁸ ms⁻¹
Firstly, convert the wavelength from nanometers to meters by multiplying by 10⁻¹: λ = 520 × 10⁻¹ m.
Using the equation for frequency (f), we get:
f = c ÷ λ = (3.00 × 10⁸ ms⁻¹) / (520 × 10⁻¹ m) = 5.77 × 10⁹ Hz
Finally, apply the equation for the maximum kinetic energy ( E kma x ):
E kma x = hf - Φ = (6.63 × 10⁻¹⁴ Js) × (5.77 × 10⁹ Hz) - (1.1 × 10⁻¹⁹ J) = 1.51 × 10⁻¹⁹ J
The maximum kinetic energy of photoelectrons is therefore 1.51 × 10⁻¹⁹ J.
The maximum kinetic energy of the photoelectrons emitted from a metal plate when illuminated with light of 520 nm wavelength is approximately 2.73 × 1 0 − 19 J . This is calculated using the energy of the photon and the work function of the metal. The steps include converting wavelength, calculating frequency, and subtracting the work function from the photon energy to find the kinetic energy.
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