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: Element Wavelength (pm) Ne 1461 Ca 335.8 Zn 143.5 Zr 78.6 Sn 49.1 (b) Plot the square root of n versus the atomic number of the element. What do you observe about the plot? (e) A particular element emits X rays with a wavelength of 98.0 pm. What element do you think it is?

Verified step by step guidance

1. 1. Moseley's law states that the frequency of the characteristic X-rays emitted by an element is proportional to the square of its atomic number (Z). The law can be written as: $\nu = a(Z - b)^2$, where $\nu$ is the frequency, $Z$ is the atomic number, $a$ and $b$ are constants.
2. 2. The frequency ($\nu$) and the wavelength ($\lambda$) of a wave are related by the equation $\nu = c/\lambda$, where $c$ is the speed of light. Therefore, we can rewrite Moseley's law in terms of wavelength: $c/\lambda = a(Z - b)^2$.
3. 3. From the given data, we can see that as the atomic number increases, the wavelength of the X-rays decreases. This is consistent with Moseley's law.
4. 4. Given that the wavelength of the X-rays emitted by the unknown element is 98.0 pm, we can compare this value with the wavelengths of the known elements. The element with the wavelength closest to 98.0 pm is likely to be the unknown element.
5. 5. By comparing the given wavelength of 98.0 pm with the provided data, we can see that it falls between the wavelengths for Zn (143.5 pm) and Zr (78.6 pm). Therefore, the unknown element is likely to be one of the elements in this range of the periodic table.

Key Concepts

Atomic Number

The atomic number of an element is defined as the number of protons in its nucleus, which determines the element's identity and its position in the periodic table. Moseley's work demonstrated that the atomic number is a more fundamental property than atomic mass, as it correlates with the X-ray wavelengths emitted by elements when they are excited.

X-ray Emission

X-ray emission occurs when high-energy electrons collide with atoms, causing inner-shell electrons to be ejected and resulting in the transition of outer-shell electrons to lower energy levels. This transition releases energy in the form of X-rays, with specific wavelengths that are characteristic of each element, allowing for the identification of elements based on their emitted X-ray wavelengths.

Wavelength and Energy Relationship

The wavelength of electromagnetic radiation is inversely related to its energy, as described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. Shorter wavelengths correspond to higher energy photons, which is crucial for understanding the X-ray emissions from elements and determining their atomic numbers based on the observed wavelengths.