Chapter 27, Problem 58A

Blue-green light has a frequency of about $6\times {10}^{14}Hz$.

a. Using the relationship $c=\lambda f$, show that its wavelength in air is $5\times {10}^{-7}m$.

b. How much larger is this wavelength than the diameter of an atom, which is about ${10}^{-10}m$?

To determine

To show the wavelength of blue-green light is 5×10-7.

Answer to Problem 58A

The wavelength of given light is 5×10-7. Hence proved.

Explanation of Solution

Given data:

Frequency (f ) = 6×10¹⁴Hz.

Formula used:

  $c=\lambda \times f$ m/s.

  $\lambda =\frac{c}{f}$ m.

Calculation:

From the given equation, we determine the formula for wave length (λ) is,

  $\lambda =\frac{c}{f}$ m.

And, we know the speed of light c =3×10⁸m/s.

Substituting the values in the equation (λ ).

  $=\frac{3\times {10}^{8}m/s}{6\times {10}^{4}Hz}$ m.

= 5×10-7 m.

Hence, it shows that the wavelength of the given light is 5×10-7 m.

Conclusion:

The wavelength of blue-green light is 5×10-7.

To determine

To calculate and compare the wavelength of light with the diameter of the atom 10-10.

Answer to Problem 58A

The size of the wavelength is 5000 times larger than the atom.

Explanation of Solution

Given data:

Diameter of atom(d ) = 10-10 m

length of wave(λ ) = 5×10-7 m

Formula used:

The difference of length of atom and the diameter of an atom.

Calculation:

The difference of length of the wave and the diameter of the atom shows the hoe much larger or smaller the wavelength of the wave with respect to the diameter of an atom.

Difference = length of wave (λ )-diameter of an atom (d )

= 5×10-7 m -10-10 m

= 5000 times.

Therefore, the wavelength is 5000 times larger than the diameter of an atom.

Conclusion:

The wavelength of blue-green light is 5000 times larger than the diameter of an atom.