What is the ratio of the wavelengths and frequencies for gold and magnesium based on their nuclear numbers?
Calculating the Ratio of Wavelengths and Frequencies for Gold and Magnesium
The wavelengths of light transmitted by different elements provide insights into their electronic transitions. In this case, we are given the nuclear numbers (Z) for gold (Au) and magnesium (Mg) as 79 and 12, respectively. We need to calculate the ratio of wavelengths and frequencies for the spectral lines of gold and magnesium based on their nuclear numbers.
Calculating the Ratio of Wavelengths:
Given:
Nuclear number of gold (Au), Z_Au = 79
Nuclear number of magnesium (Mg), Z_Mg = 12
Planck's constant, h = 6.626 × 10^-34 J·s
Speed of light, c = 3.00 × 10^8 m/s
The formula to calculate the ratio of wavelengths is:
Ratio = (Z_Mg^2 / Z_Au^2)
Substitute the values into the formula:
Ratio = (12^2 / 79^2) = 0.00229226
Therefore, the ratio of the wavelengths for gold and magnesium is approximately 0.00229226.
Calculating the Ratio of Frequencies:
The formula to calculate the ratio of frequencies is:
Ratio = λ_Mg / λ_Au = 1 / (Z_Mg^2 / Z_Au^2) = 0.870093
Therefore, the ratio of the frequencies for gold and magnesium is approximately 0.870093.
In conclusion, based on the nuclear numbers of gold and magnesium, the ratio of wavelengths is around 0.00229226, and the ratio of frequencies is around 0.870093.