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At what atomic number would a transition from n = 2 to n = 1 energy level result in emission of photon of  = 3 × 10–8 m?
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At what atomic number would a transition from n = 2 to n = 1 energy le...
Transition from n = 2 to n = 1 energy level resulting in emission of photon

To determine the atomic number at which a transition from n = 2 to n = 1 energy level results in the emission of a photon with a wavelength of λ = 3 × 10–8 m, we need to consider the energy levels and transitions involved.

1. Energy levels and transitions
- In the Bohr model of the atom, electrons occupy specific energy levels or orbits around the nucleus.
- The energy levels are labeled by quantum numbers, with the lowest energy level being n = 1, followed by n = 2, n = 3, and so on.
- When an electron transitions from a higher energy level to a lower energy level, it emits a photon with a specific wavelength corresponding to the energy difference between the two levels.

2. Energy of a photon
- The energy of a photon can be calculated using the formula E = hc/λ, where E is the energy, h is Planck's constant (6.626 × 10^(-34) J·s), c is the speed of light (3 × 10^8 m/s), and λ is the wavelength of the photon.
- Rearranging the equation, we get λ = hc/E.

3. Energy difference between energy levels
- The energy difference between two energy levels can be calculated using the formula ΔE = E2 - E1, where ΔE is the energy difference, E2 is the energy of the final level, and E1 is the energy of the initial level.
- In the Bohr model, the energy of an electron in a particular energy level is given by the equation E = -13.6 eV/n^2, where E is the energy in electron volts (eV) and n is the quantum number of the energy level.

4. Calculating the atomic number
- Let's assume the atomic number we are looking for is Z.
- For hydrogen (Z = 1), the energy difference between n = 2 and n = 1 is ΔE = -13.6 eV/2^2 - (-13.6 eV/1^2) = -10.2 eV.
- Converting -10.2 eV to joules, we get ΔE = -10.2 eV × 1.602 × 10^(-19) J/eV = -1.634 × 10^(-18) J.
- Using the equation ΔE = hc/λ, we can solve for λ: λ = hc/ΔE = (6.626 × 10^(-34) J·s × 3 × 10^8 m/s) / (-1.634 × 10^(-18) J) = 3.84 × 10^(-7) m.
- This calculated wavelength is not equal to the given wavelength of λ = 3 × 10^(-8) m, indicating that the atomic number is not 1.

Conclusion:
- The atomic number at which a transition from n = 2 to n = 1 energy level results in the emission of a photon with a wavelength of λ = 3 × 10^(-8) m is not 1.
- Further
Community Answer
At what atomic number would a transition from n = 2 to n = 1 energy le...
Λ-¹ = Z²R(1/n1² - 1/n2²)
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Attempt All sub parts from each question.Atomic Hypothesis in Ancient India and Greece Though John Dalton is credited with the introduction of atomic view point in modern science, scholars in ancient India and Greece conjectured long before the existence of atoms and molecules. In the Vaisheshika school of thought in India founded by Kanada (Sixth century B.C.) the atomic picture was developed in considerable detail. Atoms were thought to be eternal, indivisible, infinitesimal and ultimate parts of matter. It was argued that if matter could be subdivided without an end, there would be no difference between a mustard seed and the Meru mountain. The four kinds of atoms (Paramanu — Sanskrit word for the smallest particl e) postulated were Bhoomi (Earth), Ap (water), Tejas (fire) and Vayu (air) that have characteristic mass and other attributes, we re propounded. Akasa (space) was thought to have no atomic structure and was continuous and inert. Atoms combine to form different molecules (e.g. two atoms combine to form a diatomic molecule dvyanuka, three atoms form a tryanuka or a triatomic molecule), their properties depending upon the nature and ratio of the constituent atoms. The size of the atoms was also estimated, by conjecture or by methods that are not known to us. The estimates vary. In Lalitavistara, a famous biography of the Buddha written mainly in the second century B.C., the estimate is close to the modern estimate of atomic size, of the order of 10–10 m. In ancient Greece, Democritus (Fourth century B.C.) is best known for his atomic hypothesis. The word ‘atom’ means ‘indivisible’ in Greek. According to him, atoms differ from each other physically, in shape, size and other properties and this resulted in the different properties of the substances formed by their combination. The atoms of water were smooth and round and unable to ‘hook’ on to each other, which is why liquid /water flows easily. The atoms of earth were rough and jagged, so they held together to form hard substances. The atoms of fire were thorny which is why it caused painful burns. These fascinating ideas, despite their ingenuity, could not evolve much further, perhaps because they were intuitive conjectures and speculations not tested and modified by quantitative experiments–the hallmark of modern science.Q. In Greek, “atom” means

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