Question

Calculate the energy required to excite the Na electron form level n=1 to n=2. Calculate the frequency of light absorbed by Na atom in its ground state to reach this excited state. h = 6.626 x 10-34 J s

Answer 1

Answer on Question #75623 | Chemistry – General Chemistry

Calculate the energy required to excite the Na electron form level $n=1$ to $n=2$. Calculate the frequency of light absorbed by Na atom in its ground state to reach this excited state. $h = 6.626 \times 10^{-34} \, \text{J s}$

Solution

To answer this question we should use Rydberg formula for hydrogen-like chemical elements:

$$1 / \lambda = R \cdot Z ^ {2} \cdot \left(1 / n _ {1} ^ {2} - 1 / n _ {2} ^ {2}\right)$$ $$E = h \cdot v = h \cdot c / \lambda$$

Then combined equation is:

$$\Delta E = - R \cdot Z ^ {2} \cdot h \cdot c \left(1 / n _ {1} ^ {2} - 1 / n _ {2} ^ {2}\right) = - k \cdot Z ^ {2} \cdot \left(1 / n _ {1} ^ {2} - 1 / n _ {2} ^ {2}\right), \text{ where } k = 2.179 \cdot 10^{-18} \, \text{J}$$ $$\Delta E = - 2.179 \cdot 10^{-18} \cdot 11^2 \cdot \left(1 / 2^2 - 1 / 1^2\right) = 1.977 \cdot 10^{-16} \, \text{J}$$ $$v = E / h = 1.977 \cdot 10^{-16} / 6.626 \cdot 10^{-34} = 2.98 \cdot 10^{17} \, \text{s}^{-1}$$

Answer: $\Delta E = 1.977 \cdot 10^{-16} \, \text{J}, v = 2.98 \cdot 10^{17} \, \text{s}^{-1}$

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