What is the energy of a photon with a wavelength of 4.55 10-6 m? (The speed of light in a vacuum is 2.998 108 m/s. Planck's constant is 6.626 10-34 J·s.)
E = hc/wavelength
To calculate the energy of a photon, you can use the formula:
E = h * c / λ,
where:
E is the energy of the photon,
h is Planck's constant (6.626 * 10^(-34) J·s),
c is the speed of light in a vacuum (2.998 * 10^8 m/s),
λ is the wavelength of the photon.
Now, let's plug in the given values and solve the equation:
E = (6.626 * 10^(-34) J·s) * (2.998 * 10^8 m/s) / (4.55 * 10^(-6) m)
Firstly, let's multiply Planck's constant and the speed of light:
E = (6.626 * 2.998) * 10^(-34 + 8) J·m / (4.55 * 10^(-6) m)
E = 19.874748 * 10^(-26) J·m / (4.55 * 10^(-6) m)
Next, divide the J·m term by m:
E = 19.874748 / 4.55 * 10^(-26-(-6)) J
E = (19.874748 / 4.55) * 10^(6-(-26)) J
Calculating the division and exponent:
E ≈ 4.364836263 J
Therefore, the energy of a photon with a wavelength of 4.55 * 10^(-6) m is approximately 4.3648 J.