Max Speed Electron Ejected from Chromium Metal by Light of 250 nm Wavelength

[Cursed]

Homework Statement

The work function of chromium metal is 7.2 x 10^-19 J. What is the maximum speed an electron can be moving if it is ejected from chromium metal by light of wavelength 250 nm? (Answer: u= 4 x10⁵ m/s)

Homework Equations

$$\Phi = h v_{0}$$

$$KE = h v_{light} - \Phi = \frac{m_{e} u^{2}_{e}}{2}$$

$$\Delta E_{light}= \Phi + KE$$


$$h$$ is Planck's constant
$$v_{0}$$ is the characteristic frequency
$$m_e$$ is the mass of an electron (9.1 x 10^-31 kg)
$$u_e$$ is the speed of the electron

The Attempt at a Solution

$$7.2\times10^{-19} J = \frac{(9.1\times10^{-31} kg) (u^{2}_{e})}{2}$$

$$u_e \approx 1.3 \times 10^6 m/s$$

 

[Redbelly98]

Homework Statement

The work function of chromium metal is 7.2 x 10^-19 J. What is the maximum speed an electron can be moving if it is ejected from chromium metal by light of wavelength 250 nm? (Answer: u= 4 x10⁵ m/s)

Homework Equations

$$\Phi = h v_{0}$$

$$KE = h v_{light} - \Phi = \frac{m_{e} u^{2}_{e}}{2}$$

Keep this equation in mind.

$$\Delta E_{light}= \Phi + KE$$


$$h$$ is Planck's constant
$$v_{0}$$ is the characteristic frequency
$$m_e$$ is the mass of an electron (9.1 x 10^-31 kg)
$$u_e$$ is the speed of the electron

The Attempt at a Solution

$$7.2\times10^{-19} J = \frac{(9.1\times10^{-31} kg) (u^{2}_{e})}{2}$$

$$u_e \approx 1.3 \times 10^6 m/s$$

You have left out the energy of the photon, the hv_light in your earlier equation.

 

[Blueshift5]

This calculation is incorrect. The correct approach would be to use the equation KE = h v_{light} - \Phi, where KE is the kinetic energy of the ejected electron, h is Planck's constant, and v_{light} is the frequency of the light. We can rearrange this equation to solve for the maximum speed of the electron:

u_e = \sqrt{\frac{2(h v_{light} - \Phi)}{m_e}}

We can plug in the values given:

u_e = \sqrt{\frac{2((6.63\times10^{-34} J\cdot s)(3\times10^{17} s^{-1}) - (7.2\times10^{-19} J))}{9.1\times10^{-31} kg}}

u_e \approx 4 \times 10^5 m/s

Therefore, the maximum speed of the electron ejected from chromium metal by light of 250 nm wavelength is approximately 4 x 10^5 m/s.