What is the minimum work function for a metal for visible light (wavelengths between 400 and 700 ) to eject photoelectrons?
Does work function=hc divided by initial wavelength.
What would the initial wavelength be? 4x10E-7 nm?
The 400 nm photons would be the ones most capable of ejecting electrons. The work function you calculate with your formula will lead to the maximum work function that would allow ejection, not the minimum.
Work function is expressed in volts. You will have to divide the photon energy by the electron charge, e.
To determine the minimum work function for a metal to eject photoelectrons with visible light, you need to use the equation:
Energy of a photon = Planck's constant x frequency
First, you need to find the frequency of the lowest wavelength in the visible light range. The frequency of light can be calculated using the equation:
Frequency = Speed of light / Wavelength
Given that the lowest wavelength is 400 nm (or 400 x 10^-9 m), you can calculate the frequency as follows:
Frequency = (Speed of light) / (Wavelength)
= (3.00 x 10^8 m/s) / (400 x 10^-9 m)
= 7.50 x 10^14 Hz
Next, you need to calculate the energy of a photon with this frequency using Planck's constant (h):
Energy of a photon = (Planck's constant) x (Frequency)
= (6.63 x 10^-34 J·s) x (7.50 x 10^14 Hz)
= 4.97 x 10^-19 J
This energy value represents the minimum amount of energy required to eject a photoelectron from the metal's surface. It is also known as the work function of the metal.
Thus, the minimum work function for a metal to eject photoelectrons with visible light is 4.97 x 10^-19 J.
To determine the minimum work function for a metal for visible light to eject photoelectrons, we need to use the equation:
Energy of a photon = Planck's constant (h) × frequency of light (f)
Since we are given the wavelength range (400 to 700 nm), we can use the equation:
Energy of a photon = (Planck's constant × speed of light) / wavelength
The minimum work function refers to the energy required to eject a photoelectron, which is equal to the energy of a single photon. We can use the minimum wavelength (400 nm) to calculate the minimum work function.
Let's plug in the values into the equation step by step:
1. Convert the wavelength to meters:
Minimum wavelength = 400 nm = 400 × 10^(-9) meters.
2. Calculate the frequency of light using the speed of light (c = 3 × 10^8 m/s) and wavelength:
Frequency of light (f) = speed of light / wavelength = 3 × 10^8 / (400 × 10^(-9)) Hz.
3. Calculate the energy of a single photon using Planck's constant (h = 6.626 × 10^(-34) J·s) and frequency:
Energy of a photon = Planck's constant × frequency of light = 6.626 × 10^(-34) × (3 × 10^8 / (400 × 10^(-9))) J.
The result of this calculation will give you the minimum energy required to eject a photoelectron, also known as the work function of the metal for visible light.