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At what minimum atomic number, a transition from n = 2 to n = 1 energy level results in the emission of X-rays with wavelength 3.0 x 10-8 m?
    Correct answer is '2'. Can you explain this answer?
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    At what minimum atomic number, a transition from n = 2 to n = 1 energy...





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    At what minimum atomic number, a transition from n = 2 to n = 1 energy...
    Explanation:


    The energy emitted during a transition from higher energy level to lower energy level can be calculated using the formula:

    E = (hc)/λ

    where E is the energy emitted, h is Planck's constant, c is the speed of light, and λ is the wavelength of the emitted radiation.

    When an electron makes a transition from n=2 to n=1 energy level, the emitted radiation is in the form of X-rays. The minimum atomic number required for this transition to emit X-rays with a wavelength of 3.0 x 10^-8 m can be calculated as follows:

    E = (hc)/λ

    E = (6.626 x 10^-34 J·s) x (3.0 x 10^8 m/s) / (3.0 x 10^-8 m)

    E = 6.626 x 10^-16 J

    The energy difference between n=2 and n=1 energy levels can be calculated using the formula:

    ΔE = (-13.6 eV) x [(1/nf^2) - (1/ni^2)]

    where ΔE is the energy difference, nf is the final energy level (n=1), and ni is the initial energy level (n=2).

    ΔE = (-13.6 eV) x [(1/1^2) - (1/2^2)]

    ΔE = -10.2 eV

    Converting this energy to joules:

    1 eV = 1.602 x 10^-19 J

    -10.2 eV = -1.64 x 10^-18 J

    The minimum atomic number required for this transition to emit X-rays with a wavelength of 3.0 x 10^-8 m can be calculated using the formula:

    ΔE = (Z^2 x 13.6 eV) / n^2

    where Z is the atomic number and n is the initial energy level (n=2).

    -1.64 x 10^-18 J = (Z^2 x 13.6 eV) / 2^2

    Z^2 = (-1.64 x 10^-18 J x 4) / 13.6 eV

    Z^2 = -4.8 x 10^-19

    Z = 2

    Therefore, the minimum atomic number required for this transition to emit X-rays with a wavelength of 3.0 x 10^-8 m is 2.
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    At what minimum atomic number, a transition from n = 2 to n = 1 energy...
    ∆E = RhcZ2 (1/n12 – 1/n22) Here, R = 1.0967 * 107 m-1 h = 6.626 * 10-34 J sec, c = 3 * 108 m/sec n1 = 1, n2 = 2 and for H-atom, Z = 1 E2 – E1 = 1.0967 * 107 * 6.626 * 10-34 * 3 * 108(1/1 – 1/4) ∆E = 1.0967 * 6.626 * 3 * ¾ * 10-19 J = 16.3512 * 10-19 J = 16.3512 *10-19/1.6 *10-19 eV = 10.22 eV ∆E = hc/λ = RhcZ2 (1/n12 -1/n22) 1/λ = RZ2 (1/1 – 1/4) = RZ2 * 3/4 Given, λ = 3 * 10-8= m ∴ 1/3 *10-8 = 1.0967 = Z2 * 3/4 * 107 ∴ Z2 = 108 *4/3 *3 *1.0967 *107 = 40/9 *1.0967 = 4 ∴ Z = 2
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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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