Wavenumber for a radiation having 5800 Aᵒ wavelength is x × 10 cm⁻¹ The value of x is ________. (Integer answer)

Solution

Chemistry ma’am · 3 steps

Wavenumber is just 1/λ; put the wavelength in centimetres first and the rest is one division.

1. Convert to cm. 1 Å = 10⁻⁸ cm, so λ = 5800 × 10⁻⁸ cm = 5.8 × 10⁻⁵ cm.

   ν̄ = 1/λ = 1/(5.8 × 10⁻⁵ cm) = 1.7241 × 10⁴ cm⁻¹

2. Match the form. Write the result as x × 10 cm⁻¹: 17241 cm⁻¹ = 1724.1 × 10 cm⁻¹.
3. So. The integer value is x = 1724.

The common slip: 17241. Forgetting to pull out the factor of 10 gives 17241, which is the full wavenumber in cm⁻¹, not x.

The idea to keep. Wavenumber ν̄ = 1/λ, and its unit follows the length unit you use. Convert Å to cm first, then fit the answer to the power of ten the question asks for.

Answer from the NTA final answer key. Solution by PrepWiser.