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#atomic radius

13 public questions tagged with this topic.

De Broglie Hypothesis and Quantization in Bohr Model

In Rutherford’s model, what is the ratio of the size of the nucleus to the size of the atom if the nuclear radius is \(

**De Broglie hypothesis** λ = h/p, p=mv momentum, suggests electron as wave, in Bohr model circumference 2πr = n λ, standing wave condition, n wavelengths fit into orbit, for n=6, 6 wavelengths, for n=4, 4 wavelengths, explains quantization of angular momentum L = r p = r h/λ = r h n/(2πr)= n h/2π = n ħ, physical basis for Bohr quantization. Ratio = (nuclear radius/atomic radius) = (10⁻¹⁵/10⁻¹⁰) = 10⁻⁵ . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u = 931.5 MeV, evaluation yields 10⁻⁵, consistent with Bohr

Ref: NCERT > Physics Book > Atoms and Nuclei > De Broglie Hypothesis and Quantization in Bohr Model

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Bohr Model Energy Levels and Hydrogen Spectrum

The radius of the first orbit in a hydrogen atom is \( 5.3 \times 10^{-11} \, \text{m} \). What is the radius of the fif

**Excitation** energy required to go from n=1 to n=3 is 12.09 eV, from ground to n=∞ ionization 13.6 eV, state n=∞ means ionized, electron free with zero energy, highest level reached by electron beam energy determines which levels can be excited, e.g., 11 eV beam from ground can reach n=2 (10.2 eV) but not n=3 (12.09 eV), so max n=2. r_n = n² r₁ . For n = 5 : r₅ = 5² × 5.3 × 10⁻¹¹ = 25 × 5.3 × 10⁻¹¹ = 1.325 × 10⁻⁹ m . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀

Ref: NCERT > Physics Book > Atoms and Nuclei > Bohr Model Energy Levels and Hydrogen Spectrum

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Bohr Model Energy Levels and Hydrogen Spectrum

In the Bohr model, what is the ratio of the radius of the \( n = 5 \) orbit to the \( n = 1 \) orbit?

**Excitation** energy required to go from n=1 to n=3 is 12.09 eV, from ground to n=∞ ionization 13.6 eV, state n=∞ means ionized, electron free with zero energy, highest level reached by electron beam energy determines which levels can be excited, e.g., 11 eV beam from ground can reach n=2 (10.2 eV) but not n=3 (12.09 eV), so max n=2. r_n = n² r₁ . r₅ = 25 r₁ , r₁ = r₁ . Ratio = (r₅/r₁) = 25 . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u =

Ref: NCERT > Physics Book > Atoms and Nuclei > Bohr Model Energy Levels and Hydrogen Spectrum

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Hydrogen Atom Properties - Radius, Speed and Energy

In a hydrogen atom, the radius of the first orbit is \( 5.3 \times 10^{-11} \, \text{m} \). What is the circumference of

**Energy in hydrogen** total E_n = -13.6/n² eV, kinetic K = +13.6/n² eV, potential U = -27.2/n² eV, ratio K/U = -1/2, total negative indicates bound, zero at ionization, negative total means electron bound, requires energy to free. For n=4 E=-0.85 eV, U=-1.7 eV, K=0.85 eV, potential energy twice total negative. r_n = n² r₁ , r₃ = 3² × 5.3 × 10⁻¹¹ = 4.77 × 10⁻¹⁰ m . Circumference = 2π r₃ = 2 × 3.14 × 4.77 × 10⁻¹⁰ ≈ 3.0 × 10⁻⁹ m . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE

Ref: NCERT > Physics Book > Atoms and Nuclei > Hydrogen Atom Properties - Radius, Speed and Energy

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CHEMISTRY

What is the approximate ratio of the radius of an atom to its nucleus?

Rutherford’s model states the atomic radius is about 10⁻¹⁰m and the nuclear radius is 10⁻¹⁵m, giving a ratio of 10⁻¹⁰/ 10⁻¹⁵= __10POW₅__. This follows from latest NCERT 2026-27 principle explaining the concept clearly for NEET students in simple steps as per rationalized syllabus.

Ref: NCERT Chemistry Textbook - Latest Edition for Academic Session 2026-27 (Rationalized Textbook for Class XI and XII)Topic: Mole concept, atomic structure, chemical formulas like H₂O, CO₂, CH₃CH₂NH₂ and periodic trends.

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Modern Periodic Law and Present Form - Long Form Periodic Table

Which pair of elements from the same group shows the greatest increase in atomic radius?

Atomic radius increases down a group, with the largest jump often between early periods. In group 1, Li (period 2) to Na (period 3) shows a significant increase due to the addition of a new shell, compared to later pairs.

Ref: NCERT Class 11 Chemistry > Chapter 3: Classification of Elements and Periodicity in Properties > Topic: Modern Periodic Law and Present Form - Long Form Periodic Table

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