Question

Light with a wavelength of 400 nm strikes the surface of cesium in a photocell, and the maximum
kinetic energy of the electrons ejected is 1.54 x 10‐19J. Calculate the longest wavelength of light that
is capable of ejecting electrons from that metal. (1 nm = 10‐9 m)

Answer 1

Answer Question #56315 - Chemistry - Other

Question:

Light with a wavelength of $400\,\mathrm{nm}$ strikes the surface of cesium in a photocell, and the maximum kinetic energy of the electrons ejected is $1.54 \times 10^{-19}\,\mathrm{J}$. Calculate the longest wavelength of light that is capable of ejecting electrons from that metal. (1 nm = 10⁻⁹ m)

Answer:

The relation between the wavelength and energy is:

$$E = h^{\mathrm{c}} / \lambda,$$

where $h$ is the Plank’s constant, $c$ is the velocity of light (also fundamental constant), $\lambda$ is the wavelength value. Then, the minimum wavelength needed to eject the electron with the energy of $1.54 \times 10^{-19}\,\mathrm{J}$ is:

$$\lambda = h^{\mathrm{c}} / E = 6.63 \cdot 10^{-34}\,\mathrm{m^2 \cdot kg \cdot s^{-1}} \cdot 3 \cdot 10^{8}\,\mathrm{m \cdot s^{-1}} / 1.54 \cdot 10^{-19} = 12.92 \cdot 10^{-7}\,\mathrm{m} = 1292\,\mathrm{nm}$$

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