Final answer:
To find the wavelength of a photon with an energy of 7.40 × 10⁻¹¹ J, use Planck's equation and convert the result from meters to nanometers. The calculated wavelength is approximately 268 nm.
Step-by-step explanation:
Calculating the Wavelength of a Photon
To calculate the wavelength of a photon with a given energy, we can use Planck's equation, which relates the energy (E) of a photon to its frequency (ν): E = hν. Here, 'h' is Planck's constant, and 'ν' is frequency. The frequency can also be expressed in terms of the speed of light (c) and the wavelength (λ) using the relationship c = λν. By combining these equations, we obtain a formula to find the wavelength: λ = hc/E.
Given the energy of the photon is 7.40 × 10⁻¹¹ J, and using the values for Planck's constant (h = 6.626 × 10⁻4 J·s) and the speed of light (c = 3.00 × 10⁸ m/s), we can calculate the wavelength in nanometers (nm):
λ = (6.626 × 10⁻4 J·s)(3.00 × 10⁸ m/s) / (7.40 × 10⁻¹¹ J) = 2.68 × 10⁻ m.
To convert from meters to nanometers, we multiply by 10⁹ (since 1 m = 10⁹ nm), yielding a wavelength of approximately 268 nm.