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The diameter of an atom is 300 pm. How many times larger is an atom than the longest wavelength of a gamma ray?

A.
3
B.
10
C.
30
D.
300

User Madsthaks
by
8.6k points

2 Answers

3 votes

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.

User Bluehorn
by
8.6k points
6 votes

Answer:c

Step-by-step explanation:

User Brightbyte
by
7.8k points

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