Question

Moseley established the concept of atomic number by studying X rays emitted by the elements. The X rays emitted by some of the elements have the following wavelengths:

(a) Calculate the frequency, v, of the X rays emitted by each of the elements, in Hz. (b) Plot the square root of v versus the atomic number of the element. What do you observe about the plot? (c) Explain how the plot in part (b) allowed Moseley to predict the existence of undiscovered elements. (d) Use the result from part (b) to predict the X-ray wavelength emitted by iron. (e) A particular element emits X rays with a wavelength of 0.980 Å. What element do you think it is?

Using the same formula, frequencies of four other elements are calculated:

υ(Ca) = 8.928 × 10¹⁷ Hz

υ(Zn) = 2.089 × 10¹⁸ Hz

υ(Zr) = 3.81 × 10¹⁸ Hz

υ(Sn) = 6.11 × 10¹⁸ Hz

b)

The plot is linear, which allows the prediction the frequencies of new elements based on the equation of the trendline.

c) Moseley could predict the existence of undiscovered elements by filling the gaps in the plot of sqrt(v) vs. atomic number. If a new frequency is observed, it could be connected with the atomic number and in this way new element could be discovered.

d) Iron has atomic number 26.

The square root of v(iron) = 5×10⁷×(Atomic number) – 6×10⁷ = 1.24×10⁹

The frequency of radiation is 1.54×10¹⁸ Hz, and the corresponding wavelength is:

e) The frequency of 0.980 Å radiation is:

Using the graph in (b), we can calculate x if we put sqrt of v as y.

1.75×10⁹ = 5×10⁷×(Atomic number) – 6×10⁷

Atomic number = 36

The unknown element is krypton, Kr.