Asodium-vapor lamp emits yellow light at a wavelength of 589 nm. how much energy is emitted by 3.78 mg of excited sodium atoms emitting at this wavelength.

The energy emitted by sodium atoms is 33.38 j.

Explanation:

Given data:

Wavelength of photon = 589 nm   or  5.89 × 10⁻⁷m

Mass of excited sodium atoms = 3.78 mg

Energy emitted by 3.78 mg sodium atoms = ?

Solution:

First of all we we will calculate the energy of photon at given wavelength.

E = h.c/ λ

h = planck's constant =  6.626 × 10⁻³⁴  J.s

c = 3 × 10⁸ m/s

E = ( 6.626 × 10⁻³⁴  J.s × 3 × 10⁸ m/s ) / 5.89 × 10⁻⁷m

E = 19.878 × 10⁻²⁶  J.m / 5.89 × 10⁻⁷m

E =  3.375 × 10⁻¹⁹ J

Now we will calculate the number of atoms in 3.78 mg of sodium.

Mass of excited sodium = 0.00378 g  or 3.78 × 10⁻³ g

Molar mass of sodium = 23 g/mol

We know that   23 g of sodium = one mole = 6.02 × 10²³ atoms

(3.78 × 10⁻³ g / 23 g ) × 6.02 × 10²³ atoms = 0.989 × 10²⁰ atoms

The number of atoms are 0.989 × 10²⁰ atoms.

E =   0.989 × 10²⁰ × 3.375 × 10⁻¹⁹ J = 33.38 j

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