Question

What is the wavelength (in nm) of a photon if the energy is 7.26 × 10⁻¹⁹ J? (h = 6.626 × 10⁻³⁴ J • s)

Answer 1

To find the wavelength of a photon, we can use the equation E = hf and rearrange it to solve for frequency. Once we have the frequency, we can use the equation λ = c/f to calculate the wavelength. Using the given values, the wavelength of the photon is 274 nm.

Step-by-step explanation:

To find the wavelength of a photon, we can use the equation E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon. Rearranging the equation, we get f = E/h. Since we have the energy of the photon (7.26 × 10⁻¹⁹ J) and Planck's constant (6.626 × 10⁻³⁴ J · s), we can calculate the frequency. To convert the frequency to wavelength, we can use the formula c = fλ, where c is the speed of light. Rearranging the equation, we get λ = c/f. Now, we have all the values needed to calculate the wavelength.

First, calculate the frequency using f = E/h:

f = (7.26 × 10⁻¹⁹ J) / (6.626 × 10⁻³⁴ J · s) = 1.097 × 10¹⁵ Hz

Next, calculate the wavelength using λ = c/f:

λ = (3.00 × 10⁸ m/s) / (1.097 × 10¹⁵ Hz) = 2.74 × 10⁻⁷ m = 274 nm

The wavelength of the photon is 274 nm.

Answer 2

The wavelength of a photon with an energy of 7.26 × 10⁻¹⁹ J is approximately 171 nm.

Step-by-step explanation:

The wavelength (λ) of a photon can be calculated using the equation λ = c / ƒ, where c is the speed of light and ƒ is the frequency of the light. To find the wavelength in nm, we need to convert the speed of light from m/s to nm/s. The equation hc = 1240 eV · nm can be used to make this conversion.

First, we convert the energy from J to eV by dividing it by 1.602 × 10⁻¹⁹ J/eV. Then, we rearrange the equation to solve for λ and substitute the values of h (6.626 × 10⁻³⁴ J · s) and the energy in eV. Finally, we convert the wavelength from meters to nanometers by dividing by 10⁻⁹.

In this case, the energy is 7.26 × 10⁻¹⁹ J. Thus, the wavelength of the photon is approximately 171 nm.