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{:(Column I,Column II),((A)"Radius of" n...

`{:(Column I,Column II),((A)"Radius of" n^(th) "orbit",(p)"Inversely proportional to Z"),((B)"Energy of" n^(th)"orbit",(q)"Integral multiple of"(h)/(2pi)),((C)"Velocity of electron" " in " n^(th) "orbit",(r)"Proportional to n^(2)"),((D)"Angular momentum",(s)"Inversely proportional to n"),(,(t)"Inversely proportional too" n^(2)):}`

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To solve the question, we need to match the items from Column I with the correct descriptions in Column II based on the principles of Bohr's model of the atom. ### Step-by-Step Solution: 1. **Radius of n-th Orbit (A)**: - According to Bohr's model, the radius of the n-th orbit is given by the formula: \[ r_n = \frac{r_0 n^2}{Z} \] - Here, \( r_0 \) is a constant (approximately 0.53 Å), \( n \) is the principal quantum number, and \( Z \) is the atomic number. - From this formula, we can see that the radius is **inversely proportional to Z** and **proportional to \( n^2 \)**. - **Match**: A matches with P (Inversely proportional to Z) and R (Proportional to \( n^2 \)). 2. **Energy of n-th Orbit (B)**: - The energy of the electron in the n-th orbit is given by: \[ E_n = -\frac{13.6 Z^2}{n^2} \text{ eV} \] - This indicates that the energy is **inversely proportional to \( n^2 \)**. - **Match**: B matches with T (Inversely proportional to \( n^2 \)). 3. **Velocity of Electron in n-th Orbit (C)**: - The velocity of the electron in the n-th orbit is given by: \[ v_n = v_0 \frac{Z}{n} \] - Here, \( v_0 \) is a constant. This shows that the velocity is **inversely proportional to n**. - **Match**: C matches with S (Inversely proportional to n). 4. **Angular Momentum (D)**: - According to Bohr's model, the angular momentum of the electron is quantized and given by: \[ L = mvr = n\frac{h}{2\pi} \] - This indicates that angular momentum is an **integral multiple of \( \frac{h}{2\pi} \)**. - **Match**: D matches with Q (Integral multiple of \( \frac{h}{2\pi} \)). ### Final Matches: - A → P, R - B → T - C → S - D → Q

To solve the question, we need to match the items from Column I with the correct descriptions in Column II based on the principles of Bohr's model of the atom. ### Step-by-Step Solution: 1. **Radius of n-th Orbit (A)**: - According to Bohr's model, the radius of the n-th orbit is given by the formula: \[ r_n = \frac{r_0 n^2}{Z} ...
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