Final answer:
The diameter of an atom is 300 pm. An atom is approximately 0.6 times larger than the longest wavelength of a gamma ray.
Step-by-step explanation:
The diameter of an atom is 300 pm. To calculate how many times larger an atom is compared to the longest wavelength of a gamma ray, we need to convert the diameter to wavelength units. We know that wavelength = 2 * radius, so the wavelength of the atom is 600 pm. Now we can compare this to the longest wavelength of a gamma ray, which is approximately 1 femtometer (10^-15 meters).
To find how many times larger the atom is, we can divide the atom's wavelength by the wavelength of the gamma ray:
Atom to gamma ray ratio = Atom wavelength / Gamma ray wavelength = (600 pm) / (1 fm)
Simplifying the units, 1 picometer (pm) is equal to 10^-3 femtometers (fm), so we can convert the atom wavelength to femtometers:
Atom wavelength = 600 pm * (10^-3 fm/pm) = 0.6 fm
Now we can calculate the ratio:
Atom to gamma ray ratio = 0.6 fm / 1 fm = 0.6
Therefore, an atom is approximately 0.6 times larger than the longest wavelength of a gamma ray.