Question 11 (1 point)
A photon of energy 2.00 eV has a wavelength of:
Question 11 options:
A)
621 nm
B)
545 nm
C)
400 nm
D)
726 nm
E)
647 nm
B) 545 nm
To find the wavelength of a photon with a given energy, you can use the equation:
wavelength = (hc) / energy
where:
h = Planck's constant (h = 6.63 x 10^-34 J·s)
c = speed of light (c = 3.00 x 10^8 m/s)
energy = 2.00 eV = 2.00 x 1.6 x 10^-19 J
Let's calculate the wavelength using this equation:
wavelength = (hc) / energy
wavelength = (6.63 x 10^-34 J·s * 3.00 x 10^8 m/s) / (2.00 x 1.6 x 10^-19 J)
wavelength = (1.989 x 10^-25 J·m) / (3.20 x 10^-19 J)
wavelength ≈ 621 nm
Therefore, the correct answer is A) 621 nm.
To find the wavelength of a photon given its energy, you can use the relationship between energy (E) and wavelength (λ) in photon energy calculations. The formula is:
E = hc/λ
Where:
E = energy of the photon (in joules)
h = Planck's constant (6.626 x 10^-34 J·s)
c = speed of light (3.0 x 10^8 m/s)
λ = wavelength of the photon (in meters)
First, we need to convert the energy given in electron volts (eV) to joules. The conversion factor between eV and joules is:
1 eV = 1.6 x 10^-19 J
So, the energy of the photon is:
E = 2.00 eV * (1.6 x 10^-19 J/eV) = 3.2 x 10^-19 J
Now we can rearrange the formula to solve for wavelength (λ):
λ = hc/E
Substituting the values we have:
λ = (6.626 x 10^-34 J·s * 3.0 x 10^8 m/s) / (3.2 x 10^-19 J)
Calculating the expression on the right side:
λ = 5.95 x 10^-7 m
To convert this wavelength to nanometers, we divide by 10^-9 (since there are 10^9 nanometers in a meter):
λ = (5.95 x 10^-7 m) / (10^-9)
Calculating the expression:
λ = 5.95 x 10^2 nm = 595 nm
Therefore, the correct answer is not among the options provided.