Problem: The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 kJ/mol . What wavelength (in nm) of light has sufficient energy per photon to dislodge an electron from the surface of sodium?

FREE Expert Solution

$∆ E = h ν$

In the equation, the frequency of the light is used but we need wavelength. We can relate frequency and wavelength using the speed of light:

$c = λ \cdot ν \frac{c}{λ} = \frac{λ \cdot ν}{λ} ν = \frac{c}{λ}$

▪ c = speed of light = 3.0x10⁸ m/s
▪ λ = wavelength, m

Substitute in the energy equation:

$∆ E = \frac{hc}{λ} ∆ E (λ) = \frac{hc}{λ} (λ) \frac{∆ E (λ)}{∆ E} = \frac{hc}{∆ E} λ = \frac{hc}{∆ E} λ = \frac{(6.626 \times 10^{- 34} J \cdot s) (3.0 \times 10^{8} \frac{m}{s})}{275 \frac{kJ}{mol} (\frac{10^{3} J}{1 kJ}) (\frac{1 mol}{6.022 \times 10^{23} photons})}$

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Problem Details

The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 kJ/mol . What wavelength (in nm) of light has sufficient energy per photon to dislodge an electron from the surface of sodium?

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Problem: The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 kJ/mol . What wavelength (in nm) of light has sufficient energy per photon to dislodge an electron from the surface of sodium?

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