Question

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Answer 1

Answer:

1. υ = 10¹⁵ Hz

2. λ = 37.5 A°

3. υ = 3.33 × 10¹⁴ Hz

4. λ = 600 nm

Step-by-step explanation:

Given :

1. λ = 300nm ;  υ = ?

2. υ = 8 × 10¹⁶ Hz ;  λ = ? A°

3. λ = 9000 A° ;  υ = ?

4. υ = 5 × 10¹⁴ Hz ;  λ = ? nm

To find :

the question mark values

Solution :

We know that

$\boxed{\begin{array}{cc}\boxed{\mathrm{C = \lambda.\nu}}\\\text{where}\\\text{C = speed of light = 3 \times 10^8 m/s}\\\text{ \lambda = wavelength}\\\text{ \nu = frequency}\end{array}}$

1.

λ = 300nm = 300 × 10⁻⁹ m = 3 × 10⁻⁷ m

Applying the formula,

=> 3 × 10⁸ = 3 × 10⁻⁷ × υ

=> υ = 10¹⁵ Hz

________________

2.

υ = 8 × 10¹⁶ Hz

Applying the formula,

=> 3 × 10⁸ = 8 × 10¹⁶ × λ

=> λ = 3/8 × 10⁻⁸

=> λ = 30/8 × 10⁻⁹

=> λ = 3.75 × 10⁻⁹ m

=> λ = 37.5 A°

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3.

λ = 9000 A° = 9000 × 10⁻¹⁰ m = 9 × 10⁻⁷ m

Applying the formula,

=> 3 × 10⁸ = 9 × 10⁻⁷ × υ

=> υ = 1/3 × 10¹⁵ Hz

=> υ = 0.333.. × 10¹⁵ Hz

=> υ = 3.33 × 10¹⁴ Hz

____________________

4.

υ = 5 × 10¹⁴ Hz

Applying the formula,

=> 3 × 10⁸ = 5 × 10¹⁴ × λ

=> λ = 3/5 × 10⁻⁶

=> λ = 0.6 × 10⁻⁶

=> λ = 600 × 10⁻⁹ m

=> λ = 600 nm

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Some useful conversions

$\boxed{\begin{array}{cc} \mathrm{1m = 10^9\ nm}\\\mathrm{1m = 10^{10}\ A^{\circ}}\end{array}}$

Hope it helps!!