Question

A certain metal when burnt in a Bunsen flame emits light of wavelength 655 nm, calculate the Energy of light at that wavelength. (E=hv; v=c; c=2.998×10⁸ m/s; h=6.63×10⁻³⁴ J.s)

A) 3.05×10⁻¹⁹ J
B) 4.57×10⁻¹⁹ J
C) 2.42×10⁻¹⁹ J
D) 5.21×10⁻¹⁹ J

Answer 1

The energy of light at a wavelength of 655 nm is calculated using the equation E = hν, with the frequency determined from the speed of light and wavelength. The energy of light at this wavelength is approximately 3.04 × 10⁻¹⁹ J.

Step-by-step explanation:

To calculate the energy of light emitted by a metal when burnt in a Bunsen flame at a wavelength of 655 nm, we can use the equation E = hν. However, since we are given the wavelength λ, we must first find the frequency ν using ν = c / λ. Given that c (the speed of light) is 2.998×10⁸ m/s and h (Planck's constant) is 6.626×10⁻³⁴ J·s, we can proceed with the calculation.

First, convert the wavelength from nanometers to meters:
λ = 655 nm = 655 × 10⁻⁹ m.

Then, calculate the frequency ν:
ν = c / λ = (2.998×10⁸ m/s) / (655 × 10⁻⁹ m) ≈ 4.58 × 10¹⁴ Hz.

Now, apply that frequency to find the energy E:
E = hν = (6.626×10⁻³⁴ J·s) × (4.58 × 10¹⁴ Hz) ≈ 3.04 × 10⁻¹⁹ J.

Therefore, the energy of light at that wavelength is approximately 3.04 × 10⁻¹⁹ J, which makes option A) 3.05×10⁻¹⁹ J the closest answer.