Consider the following schematic plots of orbital wavefunction ($\Psi_r$) against distance ($r$) from the nucleus.
The figure representing two radial nodes in the orbital is
To determine which schematic plot represents two radial nodes in the orbital, we need to understand the concept of radial nodes in quantum chemistry. Radial nodes are the points where the radial wavefunction $\Psi_r$ becomes zero, excluding the nucleus.
For a given orbital, the total number of nodes is given by:
\(n - \ell - 1\)
where \(n\) is the principal quantum number and \(\ell\) is the azimuthal quantum number (orbital angular momentum quantum number). Radial nodes are given by \(n - \ell - 1\).
Let's analyze the schematics in the provided image:
- Plot A: The wavefunction does not cross the horizontal axis, indicating zero radial nodes.
- Plot B: The wavefunction crosses the horizontal axis once, indicating one radial node.
- Plot C: The wavefunction crosses the horizontal axis twice, indicating two radial nodes.
- Plot D: The wavefunction also crosses the horizontal axis, but in a different manner than Plot C.
Based on the analysis, Plot C has two points where $\Psi_r$ is zero (excluding the nucleus), which shows that it has two radial nodes. Therefore, the correct answer is Option C.
Similar Questions
- Given below is an expression for the rate constant of a first order reaction occurring at a certain temperature, T (K).
$\ln k = 14.34 - \frac{1.25 \times 10^4}{T}$
The energy of activation in $\text{kcal mol}^{-1}$ for the reaction is :
(Given : $k \text{ in s}^{-1}$, $R = 1.987 \text{ cal mol}^{-1} \text{ K}^{-1}$) - The number of hydrogen atoms present in $5.4 \text{ g}$ of urea is :
(Given : Molar mass of urea : $60 \text{ g mol}^{-1}$, $N_A : 6.022 \times 10^{23} \text{ particles mol}^{-1}$) For a certain reaction R $\rightarrow$ Product, the plot of [R] vs time has a negative slope as shown. The order of reaction is :
- Match List I with List II :
List I (Order of reaction) List II (Unit of rate constant) A. Zero order I. $mol^{-1} L s^{-1}$ B. First order II. $mol^{-2} L^2 s^{-1}$ C. Second order III. $s^{-1}$ D. Third order IV. $mol L^{-1} s^{-1}$
Choose the correct answer from the options given below : Calculate emf of the half cell given below :
$$Pt(s) | H_2 (g, 2 \text{ atm}) | HCl (aq, 0.02 \text{ M})$$
$$E_{H_2 /H^+}^\circ = 0 \text{ V}$$
(Given : $\frac{2.303 RT}{F} = 0.059$, $\log 2 = 0.3010$)At 298 K, a certain buffer solution contains equal concentrations of $X^{-}$ and $HX$. $K_b$ for $X^-$ is $10^{-10}$. What is the pH of this buffer solution ?
- Mixture of chloroform and acetone forms a solution with negative deviation from Raoult's law due to
- Identify the correct statements :
A. The molality of a 2.5 g of ethanoic acid (Molar mass : $60 \text{ g mol}^{-1}$) in 75 g of benzene solution is $0.556 \text{ m}$.
B. The molarity of a solution containing 5 g of NaOH (molar mass : $40 \text{ g mol}^{-1}$) in 450 mL of solution is 0.278 M at 298 K.
C. Aquatic species are more comfortable in cold water.
D. The solubility of gas increases with decrease in pressure.
E. For a binary mixture of A and B, the number of moles of A and B are $n_A$ and $n_B$ respectively, the mole fraction of B will be $x_B = \frac{n_A}{n_A + n_B}$.
Choose the correct answer from the options given below : - At a certain temperature T (K), during a process, 500 J is absorbed by the system and work of 200 J is done by the system. Then change in internal energy of the system is :
- In a qualitative analysis, $Bi^{3+}$ is detected by appearance of precipitate of $BiO(OH)(s)$. Calculate pH when the following equilibrium exists at 298 K :
$$BiO(OH) (s) \rightleftharpoons BiO^+ (aq) + OH^- (aq)$$
$K = 4 \times 10^{-10}$
(Given : $\log 2 = 0.3010$)
Important Questions from Physical Chemistry
- Consider the following electrochemical cell :
$\text{Pt} \mid \text{O}_2\text{(g)}(1\text{bar}) \mid \text{HCl(aq)} \parallel \text{M}^{2+}\text{(aq, 1.0 M)} \mid \text{M(s)}$
The pH above which, oxygen gas would start to evolve at anode is _________ (nearest integer).
Given :
$\begin{bmatrix} \text{E}^\circ_{\text{M}^{2+}/\text{M}} = 0.994 \text{ V} \\ \text{E}^\circ_{\text{O}_2/\text{H}_2\text{O}} = 1.23 \text{ V} \end{bmatrix} \text{standard reduction potential}$
and $\frac{\text{RT}}{\text{F}} (2.303) = 0.059 \text{ V}$ at the given condition - X and Y are the number of electrons involved, respectively during the oxidation of $\text{I}^-$ to $\text{I}_2$ and $\text{S}^{2-}$ to S by acidified $\text{K}_2\text{Cr}_2\text{O}_7$. The value of X + Y is ______.
- Consider two Group IV metal ions $\text{X}^{2+}$ and $\text{Y}^{2+}$.
A solution containing 0.01 M $\text{X}^{2+}$ and 0.01 M $\text{Y}^{2+}$ is saturated with $\text{H}_2\text{S}$. The pH at which the metal sulphide YS will form as a precipitate is ______. (Nearest integer)
(Given: $\text{K}_{sp}(\text{XS}) = 1 \times 10^{-22}$ at $25^\circ\text{C}$, $\text{K}_{sp}(\text{YS}) = 4 \times 10^{-16}$ at $25^\circ\text{C}$, $[\text{H}_2\text{S}] = 0.1\text{M}$ in solution, $\text{K}_{a1} \times \text{K}_{a2}(\text{H}_2\text{S}) = 1.0 \times 10^{-21}$, $\log 2 = 0.30$, $\log 3 = 0.48$, $\log 5 = 0.70$) - Electricity is passed through an acidic solution of $\text{Cu}^{2+}$ till all the $\text{Cu}^{2+}$ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping the total volume of the solution fixed at 200 mL. The total volume of oxygen evolved at STP during the entire process is ______ mL. (Nearest integer)
[Given:
$\text{Cu}^{2+}\text{(aq)} + 2\text{e}^- \rightarrow \text{Cu(s)} \quad \text{E}^\circ_{\text{red}} = +0.34 \text{ V}$
$\text{O}_2\text{(g)} + 4\text{H}^+ + 4\text{e}^- \rightarrow 2\text{H}_2\text{O} \quad \text{E}^\circ_{\text{red}} = +1.23 \text{ V}$
Molar mass of Cu = $63.54 \text{ g mol}^{-1}$
Molar mass of $\text{O}_2$ = $32 \text{ g mol}^{-1}$
Faraday Constant = $96500 \text{ C mol}^{-1}$
Molar volume at STP = 22.4 L] - Two liquids A and B form an ideal solution at temperature T K. At T K, the vapour pressures of pure A and B are 55 and $15 \text{ kN m}^{-2}$ respectively. What is the mole fraction of A in solution of A and B in equilibrium with a vapour in which the mole fraction of A is 0.8?
