Question

Consider the following three statements: (i) For any electro-magnetic radiation, the product of the wavelength and the frequency is a constant. (ii) If a source of light has a wavelength of 3.0 Å, its frequency is 1.0*1018 Hz. (iii) The speed of ultra-violet light is greater than the speed of microwave radiation. Which of these three statements is or are true?

Answer 1

Answer:

Option (i) For any electro-magnetic radiation, the product of the wavelength and the frequency is a constant.

(ii) If a source of light has a wavelength of 3.0 Å, its frequency is 1.0*1018 Hz.

Explanation:

The wave equation is given as:

$v = f\lambda$

where f  = frequency

           λ = wavelength

Thus, the product of the wavelength and frequency produces a velocity of the wave not a constant.

The velocity of the wave depends of both properties.

(ii) The wavelength of the light changes depending on the source of the radiation. Thus, the frequency is not constant or universal for one form of a wave.

Therefore statements (i) and (ii) are false.

Answer 2

Answer:

A and B

Explanation:

The relation between frequency and wavelength is shown below as:

$c=frequency\times Wavelength$

c is the speed of light having value $3\times 10^8\ m/s$

Thus, the product of the wavelength and the frequency is constant and equal to $3\times 10^8\ m/s$

Option A is correct.

Given, Frequency = $1\times 10^{18}\ Hz$

Thus, Wavelength is:

$Wavelength=\frac{c}{Frequency}$

$Wavelength=\frac{3\times 10^8}{1\times 10^{18}}\ m$

$Wavelength=3\times 10^{-10}\ m$

Also, 1 m = $3\times 10^{-10}$ Å

So,

Wavelength = 3.0 Å

Option B is correct.

As stated above, the speed of electromagnetic radiation is constant. Hence, each radiation of the spectrum travels with same speed.

Option C is incorrect.