Most Important Atomic Spectra Quiz Test Online

The first excited state corresponds to n=2. Using the formula Eₙ = -13.6/n² eV, we get E₂ = -13.6/2² = -13.6/4 = -3.4 eV.

The Balmer series ends at n_f=2. The 'second line' originates from n_i=4. Using the Rydberg formula: 1/λ = R_H (1/n_f² - 1/n_i²) = R_H (1/2² - 1/4²) = R_H (3/16). Therefore, λ = 16 / (3 R_H) ≈ 4.86 × 10⁻⁷ m, which is 486 nm.

The electron can take two paths: a direct jump (3→1) or a cascade (3→2, then 2→1). These three distinct transitions (3→1, 3→2, 2→1) produce three different spectral lines.

Transitions ending at n=5 (Pfund series) involve very small energy changes, placing these lines in the far-infrared part of the spectrum.

Helium-Neon (He-Ne) lasers produce a characteristic low-power red light, making them ideal and common for applications like barcode scanning.

The model's greatest success was its accurate prediction of the specific wavelengths of the spectral lines of hydrogen and hydrogen-like ions (those with only one electron).

When atoms are excited by collisions and then de-excite, they emit photons at specific, discrete wavelengths, creating an emission line spectrum.

Niels Bohr's key postulate was that electrons could only exist in specific, quantized energy levels, which directly explained the existence of atomic line spectra.

The energy of an electron in a hydrogen-like ion is given by E_n = -13.6 * (Z²/n²) eV. For helium, the atomic number Z=2. Ionization energy is the energy needed to remove the electron from the ground state (n=1). So, E_ion = -E₁ = -(-13.6 * (2²/1²)) = 13.6 × 4 = 54.4 eV.

The Balmer series is specifically defined as the set of transitions where the electron's final energy level is n=2.

The key principle of stimulated emission is that it produces a perfect 'clone' of the incident photon in terms of frequency, phase, and direction. This is what allows for light amplification.

A transition from a higher to a lower energy state releases a specific amount of energy, which is carried away by the emitted photon.

Shortest wavelength corresponds to the largest energy difference. For the Balmer series (ending at n=2), the largest energy drop is from the ionization limit (n = ∞).

A negative total energy signifies a 'bound state'. It means that energy must be supplied to the electron to remove it from the influence of the nucleus.

The energy levels of atoms are unique to each element. Therefore, the energy (and wavelength) of photons emitted during inner-shell transitions is a 'characteristic' of the target material.

According to classical physics, an orbiting electron should continuously radiate energy and spiral into the nucleus. The Rutherford model couldn't explain why atoms are stable.

Using the Rydberg formula, the longest Lyman wavelength (2→1) and longest Balmer wavelength (3→2) can be calculated. Their ratio λ_Lyman / λ_Balmer simplifies to 5/27.

An ordinary excited state is very unstable, and the atom will spontaneously de-excite in a very short time, typically on the order of nanoseconds (10⁻⁸ s).

The velocity of an electron in the nth orbit is inversely proportional to n (vₙ ∝ 1/n). Therefore, for n=2, the velocity is v₂ = v₁/2.

The Brackett series consists of all transitions where the electron's final energy level is n=4.

The mirrors trap photons, forcing them to pass through the active medium multiple times. This causes more stimulated emission and amplifies the light into a powerful beam.

The radius of a Bohr orbit is directly proportional to the square of the principal quantum number (rₙ ∝ n²). Therefore, the ratio r₂ / r₄ = 2² / 4² = 4 / 16 = 1/4. The ratio is 1:4.

The kinetic energy of the electron (eV) is completely converted into the energy of the highest-energy photon (hf_max = hc/λ_min). So, eV = hc/λ_min. A useful shortcut is λ_min (in nm) ≈ 1240 / V (in volts). Thus, λ_min ≈ 1240 / 50000 = 0.0248 nm, which is approximately 0.025 nm.

This is derived from equating the kinetic energy of the electron (eV) to the maximum energy of the emitted photon (hf = hc/λ).

The Paschen series ends at n=3. The 'first line' (longest wavelength) corresponds to the smallest energy jump, which is from the next level up, n=4.

For a stable orbit, the electron must form a standing wave, which means the circumference (2πr) must contain an integer number of wavelengths (nλ). This condition, 2πr = nλ, directly leads to Bohr's postulate for the quantization of angular momentum.

A short wavelength implies high frequency and high photon energy (E=hf). This high energy allows them to pass through materials that block lower-energy visible light.

While Bohr's model successfully explained the spectra of single-electron systems like H and He⁺, it failed to account for several phenomena. These include the spectra of multi-electron atoms, the relative intensities of spectral lines, and the splitting of spectral lines in magnetic (Zeeman effect) and electric (Stark effect) fields.

The energy levels are given by Eₙ = -E₀/n². As n gets larger, the energy levels get closer together, so the gap between them decreases.

In a three-level laser, the lower lasing level is the ground state, requiring over half the atoms to be pumped up. In a four-level laser, the lower lasing level is an intermediate excited state that is initially empty, making it much easier and less energy-intensive to create a population inversion.

In a three-level system, atoms are pumped to a high energy state, quickly decay to the metastable state, and then lase by transitioning from the metastable state back down to the ground state.

A ruby laser uses a powerful flash lamp (a light source) to excite the chromium ions in the ruby crystal. This method is known as optical pumping.

Since each element has a unique spectral 'fingerprint', spectroscopy is a powerful tool for chemical analysis, like determining the composition of distant stars.

Stimulated emission is the exact reverse: an incident photon causes an atom in an excited state to drop to the ground state, releasing a second photon.

The longest wavelength (lowest energy) transition in the visible Balmer series is from n=3 to n=2. This specific line is called the H-alpha line and has a prominent red color.

The electron can cascade down in multiple steps. The total number of possible unique lines is given by the formula N = (n(n-1))/2, where n is the initial state. For n=4, N = (4(4-1))/2 = (4 × 3)/2 = 6. The possible transitions are 4→3, 4→2, 4→1, 3→2, 3→1, and 2→1.

Moseley's Law states that the frequency of characteristic X-rays is proportional to the square of the atomic number (√f ∝ Z). A higher Z means the inner-shell electrons are more tightly bound, leading to larger energy differences during transitions and thus higher frequency photons.

X-rays are high-energy photons and are part of the electromagnetic spectrum, with wavelengths shorter than ultraviolet light but longer than gamma rays.

Highest frequency means highest energy (E=hf). The largest possible energy drop in a hydrogen atom is from the ionization limit (n=∞) to the ground state (n=1).

Rutherford's experiment, where alpha particles were deflected by a thin gold foil, led to the conclusion of a small, dense, positively charged nucleus.