Chemistry, 26.06.2019 17:30 ijohnh14

Determine the balmer formula n and m values for the wavelength 656.5 nm. possible choices: m= 1 n= 2 m= 2 n= 3 m= 3 n= 4 m= 2 n= 5 part b determine the balmer formula n and m values for the wavelength 486.3 nm. possible choices: m= 1 n=2 m= 2 n=3 m= 1 n=4 m= 2 n=4 part c determine the balmer formula n and m values for the wavelength 434.2 nm. possible choices: m= 1 n= 4 m= 2 n= 4 m= 3 n= 4 m= 2 n= 5 part d determine the balmer formula n and m values for the wavelength 410.3 nm. possible choices: m= 2 n= 4 m= 2 n= 5 m= 3 n= 4 m= 2 n= 6

Answers

Answer from: jeronimo18

$\boxed{\text{A. } m = 2, n = 3; \text{B. } m = 2, n = 4; \text{C. } m = 2, n = 5; \text{D. } m = 2, n = 6}$

Explanation:

The Balmer equation is

$\lambda = B\left(\dfrac{n^{2}}{n^{2} -m^{2}}\right)$

where B = 364.5 nm and m = 2

Thus, the Balmer equation reduces to

$\lambda = 364.5\left(\dfrac{n^{2}}{n^{2} - 4}\right)$

We will be doing four separate calculations for n, so it will be convenient to solve the equation for n.

$\lambda (n^{2} -4) = 364.5n^{2}\\\\\lambda n^{2} -4\lambda = 364.5n^{2}\\\\\lambda n^{2}- 364.5n^{2} = 4\lambda \\\\ n^{2}(\lambda - 364.5) = 4\lambda \\\\ n^{2}= \dfrac{4\lambda}{\lambda - 364.5}\\\\ n= \sqrt{\dfrac{4\lambda}{\lambda - 364.5}}$

A. λ = 656.5 nm

$n= \sqrt{\dfrac{4 \times 656.5}{656.5 - 364.5}} = \sqrt{\dfrac{2626}{292}} =\sqrt{8.993} = 2.999 \approx \boxed{\mathbf{3}}$

B. λ = 486.3 nm

$n= \sqrt{\dfrac{4 \times 486.3}{486.3 - 364.5}} = \sqrt{\dfrac{1945}{121.8}} =\sqrt{15.97} = 3.996 \approx \boxed{\mathbf{4}}$

C. λ = 434.2 nm

$n= \sqrt{\dfrac{4 \times 434.2}{434.2 - 364.5}} = \sqrt{\dfrac{1737}{69.7}} =\sqrt{24.9} = 4.99 \approx \boxed{\mathbf{5}}$

D. λ = 410.3 nm

$n= \sqrt{\dfrac{4 \times 410.3}{410.3 - 364.5}} = \sqrt{\dfrac{1641}{45.8}} =\sqrt{35.8} = 5.99 \approx \boxed{\mathbf{6}}$

Answer from: Quest

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Answer from: Quest

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Determine the balmer formula n and m values for the wavelength 656.5 nm. possible choices: m= 1 n=...