Question

The allowed energies of a simple atom are 0.0 eV, 4.0 eV, and 6.0 eV. Part A What wavelength(s) appear(s) in the atom's emission spectrum

Answer 1

Answer:

3.1 × 10^- 7 m and 2.1 × 10^-7 m

Explanation:

First we must convert each value of energy to Joules by multiplying its value by 1.6 ×10^-19. After that, we can now obtain the wavelength from E= hc/λ

Where;

h= planks constant

c= speed of light

λ= wavelength of light

For 6.0ev;

E= 6.0 × 1.6 ×10^-19

E= 9.6 × 10^-19 J

From

E= hc/λ

λ= hc/E

λ= 6.6 × 10^-34 × 3 × 10^8/9.6 × 10^-19

λ= 2.1 × 10^-7 m

For 4.0 eV

4.0 × 1.6 × 10^-19 = 6.4 × 10^-19 J

E= hc/λ

λ= hc/E

λ= 6.6 × 10^-34 × 3 × 10^8/6.4 × 10^-19

λ= 3.1 × 10^- 7 m

Answer 2

(a) The wavelength of the atom's emission spectrum when the energy is 4 eV is $3.1 \times 10^{-7} \ m$

(b) The wavelength of the atom's emission spectrum when the energy is 6 eV is

$2.1 \times 10^{-7} \ m$

The wavelength of the atom's emission spectrum is calculated as follows;

$E = hf\\\\E = \frac{hc}{\lambda}$

where;

• λ is the wavelength
• h is Planck's constant

For 4 eV;

$\lambda = \frac{hc}{E} \\\\\lambda = \frac{(6.626 \times 10^{-34}) \times 3\times 10^8}{4 \times 1.602 \times 10^{-19}} \\\\\lambda = 3.1 \times 10^{-7} \ m$

For 6 eV;

$\lambda = \frac{hc}{E} \\\\\lambda = \frac{(6.626 \times 10^{-34}) \times 3\times 10^8}{6 \times 1.602 \times 10^{-19}} \\\\\lambda = 2.1 \times 10^{-7} \ m$

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