Question

How do you calculate the wavelength of a photon that has an energy of `1.257 * 10^(-24)` `"J"` ?

Answer 1

You'd use the equation that establishes a relationship between energy and wavelength, which looks like this

`E = h * c/(lamda)`, where

`lamda` - the wavelength of the photon;
`c` - the speed of light, usually given as `3 * 10^(8)"m/s"`;
`h` - Planck's constant, equal to `6.626 * 10^(-34)"J s"`

Plug the value you were given for the energy of the photon in the above equation to get the wavelength

`E = h * c/(lamda) => lamda = (h * c)/E`

`lamda = (6.626 * 10^(-34)cancel("J")cancel("s") * 3 * 10^(8)"m"cancel("s"^(-)))/(1.257 * 10^(-24)cancel("J")) = color(green)(1.581 * 10^(-1)"m")`