When light of wavelength 391 nm falls on a
potassium surface, electrons are emitted that
have a maximum kinetic energy of 1.72 eV.
1) What is the cutoff wavelength of potassium?
Answer in units of nm
2)What is the threshold frequency for potassium?
Answer in units of Hz
The speed of light is 3 × 10^8 m/s and Planck’s constant is 6.63 × 10 ^−34 J · s .
KE = 1.72 eV =1.72•1.6•10^-19 =2.76•10^-19 J.
ε = h•c/λ =
=6.63•10^-34•3•10^8 /391•10^-9 = =5.08•10^-19 J
Einstein's photoelectric equation:
ε =W + KE,
Work function is
W = ε – KE =
= 5.08•10^-19 - 2.76•10^-19 =
=2.32•10^-19 J.
W = h•c/λₒ.
λₒ = h•c/W =
= 6.63•10^-34•3•10^8 /2.32•10^-19=
=8.56•10^-7 m.
W =h•fₒ.
fₒ =W/h =2.32•10^-19/6.63•10^-34 = 3.5•10^14 Hz.
this did not help at all. please come up with shorter answer. Thanks :)
To find the cutoff wavelength of potassium, we can use the equation:
Energy of a photon (E) = (Planck's constant * Speed of light) / Wavelength
Given the maximum kinetic energy (1.72 eV) and the speed of light (3 × 10^8 m/s), we need to convert the energy from electron volts to joules. The conversion factor is 1 eV = 1.6 × 10^-19 J.
1) Convert the maximum kinetic energy from electron volts (eV) to joules (J):
Maximum kinetic energy = 1.72 eV * (1.6 × 10^-19 J/eV) = 2.752 × 10^-19 J
We can rearrange the equation to solve for the cutoff wavelength (λ):
λ = (Planck's constant * Speed of light) / Energy
2) Substitute the given values into the equation:
λ = (6.63 × 10^-34 J · s * 3 × 10^8 m/s) / 2.752 × 10^-19 J
Now, we can calculate the cutoff wavelength of potassium.
3) Calculate the cutoff wavelength:
λ = 6.63 × 10^-34 J · s * 3 × 10^8 m/s / (2.752 × 10^-19 J)
λ ≈ 7.21 × 10^-7 m
To convert the cutoff wavelength to nanometers (nm), multiply by 10^9:
λ ≈ 7.21 × 10^-7 m * 10^9 nm/m
λ ≈ 721 nm
Therefore, the cutoff wavelength of potassium is approximately 721 nm.
To find the threshold frequency for potassium, we can use the equation:
Threshold frequency = Energy / Planck's constant
We already have the maximum kinetic energy in joules, so we can substitute this value into the equation.
4) Calculate the threshold frequency:
Threshold frequency = 2.752 × 10^-19 J / 6.63 × 10^-34 J · s
5) Simplify the expression:
Threshold frequency ≈ 4.15 × 10^14 Hz
Therefore, the threshold frequency for potassium is approximately 4.15 × 10^14 Hz.