What is the radius of the second Bohr orbit of \( {He}^+ \) ion?
Show Hint
158.7 pm
105.8 pm
52.9 pm
211.6 pm
The Correct Option is B
Solution and Explanation
Step 1: Use the Bohr radius formula for hydrogen-like atoms. The radius of the \( n \)-th orbit for a hydrogen-like atom is given by: \[ r_n = \frac{n^2 \hbar^2}{Z \mu e^2} \] where \( n \) is the principal quantum number, \( Z \) is the atomic number (2 for helium), \( \mu \) is the reduced mass (approximately the electron mass for light ions), \( e \) is the elementary charge, and \( \hbar \) is the reduced Planck's constant.
Step 2: Plug in the values for the second orbit (\( n = 2 \)). For the \( {He}^+ \) ion in its second orbit: \[ r_2 = \frac{4 \times 0.529 { Å}}{2} \] \[ r_2 = \frac{2.116 { Å}}{2} = 1.058 { Å} = 105.8 { pm} \]
Top AP EAMCET Chemistry Questions
- If the $pK_a$ of acetic acid and $pK_b$ of dimethylamine are $4.76$ and $3.26$ respectively, the pH of dimethyl ammonium acetate solution is
- In the first order thermal decomposition of $C _{2} H _{5} I (g) \longrightarrow C _{2} H _{4}(g)+ HI (g)$, the reactant in the beginning exerts a pressure of $2$ bar in a closed vessel at $600 \,K$. If the partial pressure of the reactant is $0.1$ bar after $1000$ minutes at the same temperature the rate constant in $\min ^{-1}$ is $(\log 2=0.3010)$
- Isopropyl benzene on aerial oxidation followed by acid hydrolysis of the resulting compound yields
- Sodium nitrite is reacted with $H_2SO_4$ to form $NaHSO_4, HNO_3$, water and $X$. Gold is dissolved in aqua-regia to form water, $AuCl^{-}_4$ and $Y. X$ and $Y$ are respectively
- The average translational kinetic energy of a molecule in a gas becomes equal to $0.69\, eV$ at a temperature about [Boltzmann constant = $1.38 \times 10^{-23} \; J \; K^{-1}$]
Top AP EAMCET Acids and Bases Questions
- If the $pK_a$ of acetic acid and $pK_b$ of dimethylamine are $4.76$ and $3.26$ respectively, the pH of dimethyl ammonium acetate solution is
- Identify the reaction in which monobasic and dibasic acids are formed
Identify the sets containing isostructural molecules from the following options:
i: \({SiF}_4\), \({CCl}_4\)
ii: \({NF}_3\), \({XeO}_3\)
iii: \({BeCl}_2\), \({HgCl}_2\)
iv: \({SF}_4\), \({XeF}_4\)One mole of compound AB reacts with one mole of compound CD according to the equation: \[ {AB} + {CD} \rightleftharpoons {AD} + {CB} \] At equilibrium, it was found that \(\frac{3}{4}\) mole of AB and CD had been converted to AD and CB. There is no change in volume. The equilibrium constant for the reaction is:
- At 298 K, the density of an aqueous solution containing 82 g of acetic acid per dm\(^3\) is 1.01 kg dm\(^{-3}\). If the molarity of the solution is \(x\) M, the molality \(m\) of the same solution is (molar mass of acetic acid = 60 g mol\(^{-1}\)):
Top AP EAMCET Questions
- If $\int \cos x . \cos 2x . \cos 5x dx = A \; \sin 2x + B \sin 4x + C \sin 6x + D \sin 8x + k $ (where $k$ is the arbitrary constant of integration), then $\frac{1}{B} + \frac{1}{C} = $
- If $k$ is one of the roots of the equation $x^2 - 25x + 24 = 0 $ such that $A = \begin{bmatrix}1&2&1\\ 3&2&3\\ 1&1&k\end{bmatrix} $ is a non-singular matrix, then $A^{-1}$ =
- If only $\frac{1}{51}^{th}$ ot the main current is to be passed through a galvanometer then the shunt required is $R_1$ and if only $\frac{1}{11}^{th}$ of the main voltage is to be developed across the galvanometer, then the resistance required is $R_2$. Then $\frac{R_2}{R_1} =$
- If $p$ and $q$ are respectively the global maximum and global minimum of the function $f(x) = x^2 e^{2x}$ on the interval $[-2, 2]$ , then $pe^{-4} + qe^4 = $
- If $\displaystyle\sum^n_{k - 1} \tan^{-1} \left( \frac{1}{k^2 + k + 1} \right) = \tan^{-1} (\theta) $ , then $\theta$ =