The value of Planck's constant is $6.63 imes 10^{-34} ext{ J s}$. The velocity of light is $3.0 imes 10^

Question

The value of Planck's constant is $6.63 	imes 10^{-34} 	ext{ J s}$. The velocity of light is $3.0 	imes 10^8 	ext{ m s}^{-1}$. The closest value to the wavelength in nanometers of a quantum of light with a frequency of $8 	imes 10^{15} 	ext{ s}^{-1}$ is:

Accepted Answer

The relationship between the speed of light ($c$), frequency ($
u$), and wavelength ($\lambda$) is given by the equation:
$$c = 
u \lambda$$
Rearranging to solve for wavelength ($\lambda$):
$$\lambda = \frac{c}{
u}$$
Given:
$c = 3.0 	imes 10^8 	ext{ m s}^{-1}$
$
u = 8 	imes 10^{15} 	ext{ s}^{-1}$

Calculation:
$$\lambda = \frac{3.0 	imes 10^8}{8 	imes 10^{15}} 	ext{ m}$$
$$\lambda = 0.375 	imes 10^{-7} 	ext{ m}$$
$$\lambda = 3.75 	imes 10^{-8} 	ext{ m}$$

To convert the wavelength into nanometers ($1 	ext{ nm} = 10^{-9} 	ext{ m}$):
$$\lambda = 3.75 	imes 10^{-8} 	ext{ m} 	imes \frac{10^9 	ext{ nm}}{1 	ext{ m}}$$
$$\lambda = 3.75 	imes 10^1 	ext{ nm}$$
$$\lambda = 37.5 	ext{ nm}$$

The closest value among the options is $4 	imes 10^1$ (which is 40).

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