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
Match List I with List II :
List I (Quantum Numbers )
$n$, $l$
List II (Orbital) A. 2, 1 I. 3d B. 4, 0 II. 2p C. 5, 3 III. 4s D. 3, 2 IV. 5f Choose the correct answer from the options given below :
- A solution of copper sulphate is electrolysed for $10 \text{ minutes}$ with a current of $1.5 \text{ amperes}$. The mass of copper deposited at cathode is :
(Given : Molar mass of Cu = $63 \text{ g mol}^{-1}$, $1 \text{ F} = 96487 \text{ C mol}^{-1}$) - 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 :
Important Questions from Physical Chemistry
$CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + CO_2(g) + H_2O(l)$
Consider the above reaction, what mass of $CaCl_2$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $CaCO_3$ ?
(Given: Molar mass of Ca, C, O, H and Cl are 40, 12, 16, 1 and 35.5 g $mol^{-1}$, respectively)- According to Bohr's model of hydrogen atom, which of the following statement is incorrect?
Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?Which of the following graphs correctly represents the plot of $K_H$ at 1 bar for gases in water versus temperature?
If equal volumes of $AB_2$ and $XY$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $AY_2$ at 300 K ?
(Given $K_{sp}$ (at 300 K) for $AY_2=5.2 \times 10^{-7}$)
