Question

in a hypothetical element ,two energy levels are separated by an energy of 282kj mol-1 . what wavelength of light (in nma) is evolved for an electron to change between these two levels?​

Answer 1

7.05 × 10⁻²² nm

Step-by-step explanation:

Step 1: Given and required data

• Energy evolved when a mole of electrons changes between the 2 levels (E): 282 kJ

• Planck's constant (h): 6.63 × 10⁻³⁴ J.s

• Speed of light (c): 3.00 × 10⁸ m/s

Step 2: Calculate the wavelength (λ) of the light evolved

We will use Planck-Einstein's relation.

E = h × c/λ

λ = h × c/E

λ = (6.63 × 10⁻³⁴ J.s) × (3.00 × 10⁸ m/s)/(282 × 10³ J) = 7.05 × 10⁻³¹ m

We will convert λ to nm using the conversion factor 1 m = 10⁹ nm.

7.05 × 10⁻³¹ m × 10⁹ nm/1 m = 7.05 × 10⁻²² nm