A carbon atom is bombarded by high energy photons with a wavelength of 40 nm. Find how many electrons are ejected and the velocity of the first electron.
To determine the number of electrons ejected and the velocity of the first electron when a carbon atom is bombarded by high energy photons, we need to use the equation for the energy of a photon and the quantum concept of the photoelectric effect.
1. Calculate the energy of a photon:
The energy of a photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J⋅s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength of the photon (40 nm = 40 x 10^-9 m).
Substituting the values into the equation:
E = (6.626 x 10^-34 J⋅s)(3.0 x 10^8 m/s)/(40 x 10^-9 m)
2. Calculate the energy required to remove an electron from a carbon atom:
To remove an electron from a carbon atom, we need the ionization energy of carbon. The ionization energy is the minimum energy required to completely remove an electron from an atom. For carbon, the ionization energy is approximately 11.26 eV (electron volts) or 1.805 x 10^-18 J.
3. Determine the number of photons required to eject an electron:
The number of photons required to eject an electron can be calculated by dividing the energy required to remove an electron from the carbon atom by the energy of a single photon.
Number of photons = (Energy required to remove an electron)/(Energy of a single photon)
4. Calculate the velocity of the first electron:
The velocity of the electron can be determined using the equation KE = 1/2 mv^2, where KE is the kinetic energy, m is the mass of the electron (9.10938356 x 10^-31 kg), and v is the velocity of the electron.
Solving for the velocity, we can rearrange the equation as v = sqrt(2KE/m).
Now, let's perform the calculations:
Step 1:
E = (6.626 x 10^-34 J⋅s)(3.0 x 10^8 m/s)/(40 x 10^-9 m)
Step 2:
Ionization energy of carbon = 1.805 x 10^-18 J
Step 3:
Number of photons = (1.805 x 10^-18 J)/(energy of a single photon)
Step 4:
v = sqrt(2KE/m)
By evaluating these calculations, we can find the number of ejected electrons and the velocity of the first electron.