Chapter 6, Problem 110AP

Interpretation Introduction

Interpretation:

The wavelength of light emitted in the transition from the first excited energy state to ground state of a certain element is to be determined, with given ionization energy of element.

Concept introduction:

Wavelength is the separation between two progressive crests or troughs.

The energy of a photon can be expressed as

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

Here, $E$ denotes the energy of photon, $\text{h}$ denotes Planck’s constant $\left(6.63\times {10}^{-34}\text{ J}\cdot \text{s}\right)$, $\text{c}$ denotes the speed of light $\left(3.0\times {10}^8\text{ m/s}\right)$, and $\lambda$ denotes the wavelength.

The emission energy of photon (E) when it moves from the first excited state to ground state can be calculated as

$E=E_1-E_2$

The relationship between meter and nanometer can be expressed as: $1\text{ nm}=1\times {10}^{-9}\text{ m}$

To convert meter to nanometer, conversion factor is $\frac{1\text{ nm}}{1\times {10}^{-9}\text{ m}}$.

The relationship between number of moles and number of atoms can be expressed as $1\text{ mol}=6.022\times {\text{ 10}}^{23}\text{atoms}$

To convert number of atoms to number of moles, conversion factor is $\frac{1\text{ mol}}{6.022\times {10}^{23}}$.

The relationship between kilojoules and joules can be expressed as $1\text{kJ}=1000\text{ J}$.

To convert kilojoules to joules, conversion factor is $\frac{1000\text{ J}}{\text{ kJ}}$.