A certain kind of light has a wavelength of 4.6 micrometers what is the frequency of this light and gigahertz? Use c= 2.998 × 10^8 m/s for the speed of light. ​

6.52×10⁴ GHz

Explanation:

From the question given above, the following data were obtained:

Wavelength (λ) = 4.6 μm

Velocity of light (v) = 2.998×10⁸ m/s

Frequency (f) =?

Next we shall convert 4.6 μm to metre (m). This can be obtained as follow:

1 μm = 1×10¯⁶ m

Therefore,

4.6 μm = 4.6 μm × 1×10¯⁶ m / 1 μm

4.6 μm = 4.6×10¯⁶ m

Next, we shall determine frequency of the light. This can be obtained as follow:

Wavelength (λ) = 4.6×10¯⁶ m

Velocity of light (v) = 2.998×10⁸ m/s

Frequency (f) =?

v = λf

2.998×10⁸ = 4.6×10¯⁶ × f

Divide both side by 4.6×10¯⁶

f = 2.998×10⁸ / 4.6×10¯⁶

f = 6.52×10¹³ Hz

Finally, we shall convert 6.52×10¹³ Hz to gigahertz. This can be obtained as follow:

1 Hz = 1×10¯⁹ GHz

Therefore,

6.52×10¹³ Hz = 6.52×10¹³ Hz × 1×10¯⁹ GHz / 1Hz

6.52×10¹³ Hz = 6.52×10⁴ GHz

Thus, the frequency of the light is 6.52×10⁴ GHz

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