Question

Which of the following statements is correct? (1) Rydberg constant is same for all elements. (2) Line spectra is characteristic of molecules. (3) Transition of electron from \(n=3\) to \(n=1\) level results in band spectrum. (4) The continuum of atomic spectrum is due to ionisation of atom.

Short answer

The continuum of atomic spectrum is due to ionisation of atom.

Step-by-step solution

Understand the Statements

Review each statement carefully to understand its meaning about atomic and molecular spectra.

Analyze Statement (1)

Consider if the Rydberg constant is the same for all elements. The Rydberg constant is actually different for different elements as it depends on the nucleus charge (proton number), so this statement is incorrect.

Analyze Statement (2)

Evaluate if line spectra are characteristic of molecules. Line spectra are characteristic of atoms, not molecules. Therefore, this statement is incorrect.

Analyze Statement (3)

Examine if the transition of an electron from a higher to a lower energy level (e.g., from n=3 to n=1) results in a band spectrum. Such transitions produce line spectra, not band spectra, so this statement is incorrect.

Analyze Statement (4)

Determine if the continuum of an atomic spectrum is due to the ionization of the atom. Ionization results in a continuum spectrum as it involves the absorption/emission of a wide range of wavelengths, removing the electron completely from the atom. This statement is correct.

Key concepts

Rydberg constant

The Rydberg constant is an important value in atomic physics, used primarily in the calculation of wavelengths of spectral lines of many chemical elements. It is denoted by the symbol \(R_\infty\) and its value is approximately 1.097 × 10^7 m^(-1). This constant varies slightly for different elements because it is dependent on the nucleus charge, or the number of protons in the atomic nucleus. Therefore, the Rydberg constant for hydrogen differs slightly from that of heavier elements due to differences in nuclear mass and charge.

Line spectra

Line spectra are unique patterns of light emission or absorption specific to individual atoms. Unlike continuous spectra, which show an unbroken spread of colors or wavelengths, line spectra consist of discrete lines that correspond to specific energy changes within an atom. These lines result from electrons moving between energy levels, absorbing or emitting photons of precise wavelengths. Line spectra are characteristic of individual atoms, making them useful for identifying elements in substances and determining atomic structures.

Electron transition

Electron transitions occur when an electron in an atom moves from one energy level to another. This can happen by absorbing a photon (gaining energy) or emitting a photon (losing energy). The energy difference between the initial and final levels determines the photon's wavelength and, consequently, the color of light in the emission or absorption spectrum. For instance, a transition from the \(n=3\) to the \(n=1\) level in hydrogen releases a photon in the ultraviolet range, resulting in a line in the line spectrum. These transitions help explain the discrete nature of the spectral lines observed.

Ionization spectrum

The ionization spectrum refers to the continuum spectrum created when an atom is ionized—meaning one or more of its electrons are completely removed. This process absorbs or emits energy over a wide range of wavelengths, rather than at distinct energy levels, leading to a continuous spread of spectral lines. Ionization occurs at the point where the energy of the incoming photon or energy source equals or surpasses the ionization energy of the given atom, completely freeing an electron and resulting in a continuous spectrum rather than the distinct lines seen in typical electronic transitions within atoms.