Question

Select the correct answer. The radius of a nitrogen atom is 5. 6 × 10-11 meters, and the radius of a beryllium atom is 1. 12 × 10-10 meters. Which atom has a larger radius, and by how many times is it larger than the other? A. The radius of nitrogen is 20 times larger than the radius of beryllium. B. The radius of beryllium is 40 times larger than the radius of nitrogen. C. The radius of nitrogen is 4 times larger than the radius of beryllium. D. The radius of beryllium is 2 times larger than the radius of nitrogen.

Answer 1

A negative exponent means the number of the exponent divide by the number. The the radius of beryllium atom is larger than the radius of a nitrogen atom by two times.

Given information-

The radius of a nitrogen atom is $5.6\times10^{-11}$ meters.

The radius of a beryllium atom is $1.12 \times10^{-10}$ meters

Negative exponents

A negative exponent means the number of the exponent divide by the number.

As the radius of the nitrogen atom is $5.6\times10^{-11}$ meters. Convert it in the power of negative exponent of 10.

Let the radius of the nitrogen is $r$ mm. Thus,

$r=5.6\times 10^{-11}\\ r=5.6\times 10^{-10-1}\\ r=5.6\times 10^{-10}\times10^{-1}\\ r=\dfrac{5.6\times 10^{-10}}{10} \\ r=0.56\times 10^{-10}$

Now the base of the exponents of both the atoms are same. As the radius of the nitrogen atom is $0.56\times 10^{-10}$ meters and the radius of the beryllium atom is $1.12 \times10^{-10}$. Thus the radius of beryllium atom is larger.

To calculate how many times, the radius of beryllium atom should be divided by the radius of a nitrogen atom. Thus,

$=\dfrac{1.12\times10^{-10}}{0.56\times10^{-10}} \\ =2$

Thus the the radius of beryllium atom is larger than the radius of a nitrogen atom by two times.

Learn more about the negative exponents here;

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