Question

Consider the four scenarios involving visible light. In scenario A, visible light has a wavelength of 715.3 nm. Determine its frequency, energy per photon, and color.

Answer 1

Answer:

1. frequency (f) = 4.194 × 10^14Hz

2. Energy of photon (E) = 2.779 × 10^-19 J

3. Color is RED

Explanation:

1. Based on the information in this question, a visible light has a wavelength of 715.3 nm.

λ = v/f

Where; λ = wavelength (nm)

v = speed of light (3 × 10^8m/s)

f = frequency (Hz)

f = v/λ

f = 3 × 10^8/715.3 × 10^-9

f = 0.004194 × 10^(8+9)

f = 0.004194 × 10^17

f = 4.194 × 10^14Hz

2. Energy per photon is calculated thus;

E = hf

Where; E = energy of photon (J)

h = Planck's constant (6.626 × 10^-34 J/s)

f = frequency (Hz)

E = 6.626 × 10^-34 × 4.194 × 10^14

E = 27.789 × 10^(-34+14)

E = 27.789 × 10^-20

E = 2.779 × 10^-19 J

3. Based on the wavelength range of the visible spectrum, wavelength of 715.3nm falls between 625-740nm, which is RED color of light. Hence, the color of the visible light is RED.

Answer 2

The frequency is "$419.5\times 10^{12} \ s^{-1}$", energy per photon is "$2.780\times 10^{-19} \ J$" and the color is "red".

Given:

Wavelength,

• $\lambda = 715.1 \ nm$

or,

           $= 715.1 \ nm\times (10^-9 \ m/nm)$

As we know the formula,

→ $Frequency = \frac{Speed \ of \ light}{wavelength}$

By substituting the values, we get

                    $= \frac{(3\times 10^8) }{715.1\times 10^{-9} }$

                    $= 419.5\times 10^{12} \ s^{-1}$  

Now,

The energy per photon will be:

→ $E = Planck's \ constant\times Frequency$

      $= 6.626\times 10^{-34}\times 419.5\times 10^{12}$

      $= 2.780\times 10^{-19} \ J$

Thus the above answer is correct.

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