Question

light travels (in vacuum) at a velocity of 3 x 10 ^8 m/s. The lowest visible wavelength is 420 nanometers ( 1 nanometer = 1 x 10^-9) Calculate the corresponding frequency for that wavelength.

Answer 1

We know, frequency of light wave = speed of light in vaccum / wavelength

That is ν = c / λ

Therefore for wavelength,λ = 420nm = 420 * 10^-9m and speed of light,c = 3* 10^8m/s,

We have ν= (3*10^8 m/s) / (420*10^-9 m)

ν = 7.143 * 10^14 Hertz. Answer

Answer 2

 Calculation:

1. Key Formula:

The speed of light ($c$), wavelength ($\lambda$), and frequency ($f$) are related by:

$$c=\lambda \times f\text{or}f=\frac{c}{\lambda }$$

• Speed of light ($c$): $3\times 10^8\text{m/s}$

• Wavelength ($\lambda$): $420\text{nm}$ (convert to meters first!).

• 
  

2. Convert Wavelength to Meters:

$$1\text{nm}=10^{-9}\text{m}⟹420\text{nm}=420\times 10^{-9}\text{m}=4.2\times 10^{-7}\text{m}$$

3. Plug into the Formula:

$$f=\frac{c}{\lambda }=\frac{3\times 10^8\text{m/s}}{4.2\times 10^{-7}\text{m}}=\frac{3}{4.2}\times 10^{8+7}\text{Hz}$$$$f=0.714\times 10^{15}\text{Hz}=7.14\times 10^{14}\text{Hz}$$

4. Simplify (Optional):

• $7.14\times 10^{14}\text{Hz}=714\text{THz}$ (terahertz).

 

1. Answer: 7.14 × 10¹⁴ Hz.