Question

Which from following colours has highest energy if wave lengths of violet, blue, yellow and red light are 410 nm, 470 nm, 580 nm and 750 nm respectively ?

• A. Blue
• B. Violet
• C. Yellow
• D. Red

Hint:

Energy of a photon is inversely proportional to wavelength, so pick the shortest wavelength.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Light of a given colour has a photon energy fixed by its wavelength. The shorter the wavelength, the higher the frequency and the higher the energy of each photon.

Step 2: Key Formula or Approach:
\[ E = h\nu = \frac{hc}{\lambda} \]
Here \(h\) and \(c\) are constants, so \(E \propto \dfrac{1}{\lambda}\). The colour with the smallest wavelength has the largest energy.

Step 3: Detailed Explanation:
The given wavelengths are violet 410 nm, blue 470 nm, yellow 580 nm and red 750 nm.
Violet has the smallest wavelength, 410 nm, so it has the largest value of \(1/\lambda\).
Energy ratio of violet to red: \(\dfrac{750}{410} \approx 1.83\), so a violet photon carries almost twice the energy of a red photon.
Blue (470 nm) is higher in energy than yellow and red but lower than violet. Yellow (580 nm) and red (750 nm) have longer wavelengths, so their energies are smaller still.

Final Answer:
Violet light has the shortest wavelength, so it has the highest energy. This is option (B). \[ \boxed{\text{Violet (B)}} \]