Light of wavelength 272 nm shines on a piece of magnesium metal. What is the speed of the ejected electron? (Light energy greater than that of the work function of magnesium ends up as kinetic energy of the ejected electron. The work function is the minimum energy needed to eject an electron from the metal by irradiating it with light. The photoelectric work function for magnesium is 5.90 10-19 J.)
Energyphoton-workfunction=KE ejected electron
So what portion of this do you need help with? Consider Planck's equation.
I need solution
To find the speed of the ejected electron, we first need to determine the energy of the incident light using its wavelength, and then calculate the kinetic energy of the ejected electron.
1. Calculate the energy of the incident light:
- We know the wavelength of the light is 272 nm.
- The energy (E) of a photon can be calculated using the equation:
E = h * c / λ
where h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of light in meters.
- Convert the given wavelength (272 nm) to meters by dividing by 10^9, since 1 nm = 10^-9 m.
- Substitute the values into the equation to find the energy of the incident light.
2. Calculate the kinetic energy of the ejected electron:
- The kinetic energy (KE) of the ejected electron can be calculated using the equation:
KE = E - W
where E is the energy of the incident light and W is the work function.
- Substitute the values obtained in step 1 into the equation to find the kinetic energy.
3. Calculate the speed of the ejected electron:
- The kinetic energy of the ejected electron can be expressed as:
KE = (1/2) * m * v^2
where m is the mass of the electron (9.11 x 10^-31 kg) and v is the speed of the electron.
- Rearrange the equation to solve for v.
Now let's calculate the speed of the ejected electron step by step.
Step 1:
λ = 272 nm = 272 x 10^-9 m
E = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (272 x 10^-9 m)
Step 2:
KE = E - W
where W = 5.90 x 10^-19 J
Step 3:
KE = (1/2) * m * v^2
Solve for v