If the energy of a photon is 1.32 × 10^-18 J, what is its wavelength in nm?
To calculate the wavelength of a photon, you can use the formula:
wavelength = (speed of light) / (frequency)
The speed of light is a constant value, approximately equal to 3.00 x 10^8 meters per second (m/s). However, the given energy of the photon is in joules (J), so we need to find the frequency first.
The energy of a photon can also be expressed using Planck's equation:
energy = (Planck's constant) x (frequency)
Planck's constant is approximately equal to 6.63 x 10^-34 joule-seconds (J·s). Rearranging the equation, we can solve for the frequency:
frequency = energy / Planck's constant
Substituting the given energy value of 1.32 x 10^-18 J and Planck's constant, we can calculate the frequency. Then, we can substitute the frequency value into the first equation to find the wavelength.
Let's plug in the values and solve step-by-step:
Step 1: Calculate the frequency
frequency = (1.32 x 10^-18 J) / (6.63 x 10^-34 J·s)
frequency ≈ 1.99 x 10^15 Hz
Step 2: Calculate the wavelength
wavelength = (speed of light) / (frequency)
wavelength = (3.00 x 10^8 m/s) / (1.99 x 10^15 Hz)
To convert meters to nanometers (nm), we need to multiply the value by 10^9 since 1 meter equals 10^9 nanometers.
wavelength = [(3.00 x 10^8 m/s) / (1.99 x 10^15 Hz)] * (10^9 nm/m)
wavelength ≈ 1.51 nm
Therefore, the wavelength of the photon is approximately 1.51 nm.
E = hf = h * c/λ
So solve for λ