Question

An angstrom (symbol$\stackrel{\circ }{A}$) is a unit of length, defined as${10}^{-10}\mathrm{m}$, which is on the order of the diameter of an atom.

(a) How many nanometres are there in 1.0 angstrom?

(b) How many femtometers or fermis (the common unit of length in nuclear physics) are there in 1.0 angstrom?

(c) How many angstroms are there in 1.0 m?

(d) How many angstroms are there in 1.0 light-year (See problem 19)?

Short answer

(a) 1.0 angstrom is equal to 0.1 nanometer.

(b) 1.0 angstrom is equal to ${10}^5$femtometers.

(c) 1.0 meter is equal to ${10}^{10}$angstroms.

(d) 1.0 light-year is equal to $9.46\times {10}^{25}$angstroms.

Step-by-step solution

Step 1. Definition of a light-year

Light-year denotes the distance traveled by light in one year.

Step 2. Given data and assumption

The relation between meter and angstrom unit is $1\stackrel{\circ }{A}=1\times {10}^{-10}\mathrm{m}$.

Step 3. Calculating nanometres in 1.0 angstrom

By the definition of a nanometre, you can write

$1\mathrm{nm}={10}^{-9}\mathrm{m}$.

Dividing by 10 on both sides,

localid="1643875930233" $0.1\mathrm{nm}={10}^{-10}\mathrm{m}$.

By using the relationship between angstrom and meter,

$0.1\mathrm{nm}=1\stackrel{\circ }{A}$.

Thus, 1.0 angstrom is equal to 0.1 nanometer.

Step 4. Calculating the femtometers in 1.0 angstrom

By the definition of a femtometer, you can write

$1\mathrm{fm}={10}^{-15}\mathrm{m}$.

Multiplying by ${10}^5$on both sides,

localid="1643875945843" ${10}^5\mathrm{fm}={10}^{-10}\mathrm{m}$.

By using the relationship between angstrom and meter,

${10}^5\mathrm{fm}=1\stackrel{\circ }{\mathrm{A}}$.

Thus, 1.0 angstrom is equal to ${10}^5$femtometers.

Step 5. Calculating the angstroms in 1.0 meter

You know that

$1\stackrel{\circ }{A}=1\times {10}^{-10}\mathrm{m}$.

Multiplying by ${10}^{10}$on both sides,

${10}^{10}\stackrel{\circ }{A}=1\mathrm{m}$.

Thus, 1 meter is equal to ${10}^{10}$angstroms.

Step 6. Calculating the angstroms in 1.0 light-year

By the definition of a light-year, you can write

$1\mathrm{light}-\mathrm{year}=9.46\times {10}^{15}\mathrm{m}$.

The above equation can be re-written as

localid="1643875839836" $1\mathrm{light}-\mathrm{year}=\left(9.46\times {10}^{25}\right)\times {10}^{-10}\mathrm{m}$.

Using the definition of 1.0 angstrom, you can write the above equation as

localid="1654697858854" $1\mathrm{light}-\mathrm{year}=\left(9.46\times {10}^{25}\right)\stackrel{\circ }{A}$.

Thus, there are $9.46\times {10}^{25}$angstroms in 1.0 light-year.