Explanation Write the expression for wave function for n = 2 and l = 0 . ψ = 1 4 2 π ( 1 a 0 ) 3 2 ( 2 − r a 0 ) e − r 2 a 0 (I) Here, ψ is the wave function, a 0 is the Bohr radius and r is the radius of the nucleus. Write the condition for the most probable distance from the nucleus. d [ r ⋅ ψ ] d r = 0 (II) Substitute 1 4 2 π ( 1 a 0 ) 3 2 ( 2 − r a 0 ) e − r 2 a 0 for ψ in equation (II) to find most probable distance from the nucleus. d [ r { 1 4 2 π ( 1 a 0 ) 3 2 ( 2 − r a 0 ) e − r 2 a 0 } ] d r = 0 1 4 2 π ( 1 a 0 ) 3 2 d [ ( 2 r − r 2 a 0 ) e − r 2 a 0 ] d r = 0 Differentiating the above equation with respect to r

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

See similar textbooks

Concept explainers

Atomic Spectra

According to the Bohr model of an atom, the electron in an atom moves around a nucleus in fixed orbits with specific energies known as energy levels. The orbital energies are quantized. The electrons remain in these energy levels until they emit or absor…

Ruby Lasers

Lasers are devices that emit light using atoms or molecules at a certain wavelength and amplify the light to produce a narrow beam of radiation. It works as per the principle of electromagnetic radiation. Their source of emission contains the same freque…

Balmer Series

The spectrum of frequency observed when electromagnetic radiation is emitted from an atom when it goes from higher energy state to lower state, is known as emission spectrum. This transition occurs when an excited electron moves from higher to lower stat…

Emission Spectrum

Every state of matter tries to be at minimum potential energy or it can be said that the atoms of element/ substance arrange themselves such that overall energy is minimum.

Question

Chapter 39, Problem 67GP

To determine

The most probable distance from the nucleus of an electron in the n=2, l=0 state of hydrogen.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 39, Problem 66GP

Chapter 39, Problem 68GP

Students have asked these similar questions

If an electron is in the ground state of the hydrogen atom, the probability that its distance from the proton is more than one Bhor radius is approximately 1. 0.68 2. 0.48 3. 0.28 4. 0.91

Determine the integral | P(r) dr for the radial probability density for the ground state of the hydrogen atom 4 P(r) = - r²e-2rla a³ O 1 O-1 O 0.5

How many different possible states can there be for an atom with n =5 and l = 1 ?

Chapter 39 Solutions

Physics for Scientists and Engineers with Modern Physics

Ch. 39.2 - Prob. 1AE Ch. 39.2 - Prob. 1BE Ch. 39.3 - Prob. 1CE Ch. 39.4 - Prob. 1DE Ch. 39.4 - Prob. 1EE Ch. 39.5 - Prob. 1FE Ch. 39.7 - Prob. 1GE Ch. 39 - Prob. 1Q Ch. 39 - Prob. 2Q Ch. 39 - Prob. 3Q

Ch. 39 - Prob. 4Q Ch. 39 - Prob. 5Q Ch. 39 - Prob. 6Q Ch. 39 - Prob. 7Q Ch. 39 - Prob. 8Q Ch. 39 - Prob. 9Q Ch. 39 - Prob. 10Q Ch. 39 - Prob. 11Q Ch. 39 - On what factors does the periodicity of the...Ch. 39 - Prob. 13Q Ch. 39 - Prob. 14Q Ch. 39 - Prob. 15Q Ch. 39 - Prob. 16Q Ch. 39 - Prob. 17Q Ch. 39 - Prob. 18Q Ch. 39 - Prob. 19Q Ch. 39 - Prob. 20Q Ch. 39 - Prob. 21Q Ch. 39 - Prob. 22Q Ch. 39 - Prob. 23Q Ch. 39 - Prob. 24Q Ch. 39 - Prob. 25Q Ch. 39 - Prob. 26Q Ch. 39 - Prob. 27Q Ch. 39 - Prob. 28Q Ch. 39 - Prob. 29Q Ch. 39 - Prob. 1P Ch. 39 - Prob. 2P Ch. 39 - Prob. 3P Ch. 39 - Prob. 4P Ch. 39 - Prob. 5P Ch. 39 - Prob. 6P Ch. 39 - Prob. 7P Ch. 39 - Prob. 8P Ch. 39 - Prob. 9P Ch. 39 - Prob. 10P Ch. 39 - Prob. 11P Ch. 39 - Prob. 12P Ch. 39 - Prob. 13P Ch. 39 - Prob. 14P Ch. 39 - Prob. 15P Ch. 39 - Prob. 16P Ch. 39 - Prob. 17P Ch. 39 - Prob. 18P Ch. 39 - Prob. 19P Ch. 39 - Prob. 20P Ch. 39 - Prob. 21P Ch. 39 - Prob. 22P Ch. 39 - Prob. 23P Ch. 39 - Prob. 24P Ch. 39 - Prob. 25P Ch. 39 - Prob. 26P Ch. 39 - Prob. 27P Ch. 39 - Prob. 28P Ch. 39 - Prob. 29P Ch. 39 - Prob. 30P Ch. 39 - Prob. 31P Ch. 39 - Prob. 32P Ch. 39 - Prob. 33P Ch. 39 - Prob. 34P Ch. 39 - Prob. 35P Ch. 39 - Prob. 36P Ch. 39 - Prob. 37P Ch. 39 - Prob. 38P Ch. 39 - Prob. 39P Ch. 39 - Prob. 40P Ch. 39 - Prob. 41P Ch. 39 - Prob. 42P Ch. 39 - Prob. 43P Ch. 39 - Prob. 44P Ch. 39 - Prob. 45P Ch. 39 - Prob. 46P Ch. 39 - Prob. 47P Ch. 39 - Prob. 48P Ch. 39 - Prob. 49P Ch. 39 - Prob. 50P Ch. 39 - Prob. 51P Ch. 39 - Prob. 52P Ch. 39 - Prob. 53P Ch. 39 - Prob. 54P Ch. 39 - Prob. 55P Ch. 39 - Prob. 56P Ch. 39 - Prob. 57P Ch. 39 - Prob. 58P Ch. 39 - Prob. 59P Ch. 39 - Prob. 60P Ch. 39 - Prob. 61GP Ch. 39 - Prob. 62GP Ch. 39 - Prob. 63GP Ch. 39 - Prob. 64GP Ch. 39 - Prob. 65GP Ch. 39 - Prob. 66GP Ch. 39 - Prob. 67GP Ch. 39 - Prob. 68GP Ch. 39 - Prob. 69GP Ch. 39 - Prob. 70GP Ch. 39 - Prob. 71GP Ch. 39 - Prob. 72GP Ch. 39 - Prob. 73GP Ch. 39 - Prob. 74GP Ch. 39 - Prob. 75GP Ch. 39 - Prob. 76GP Ch. 39 - Prob. 77GP

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

The most probable distance from the nucleus of an electron in the n = 2 , l = 0 state of hydrogen.

Concept explainers

The most probable distance from the nucleus of an electron in the n=2, l=0 state of hydrogen.

Want to see the full answer?

Chapter 39 Solutions