/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 30 If photons of energy \(12.75 \ma... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 30

If photons of energy \(12.75 \mathrm{eV}\) are passing through hydrogen gas in ground state then number of lines in emission spectrum will be (A) 6 (B) 4 (C) 3 (D) 2

Short Answer

Expert verified
The number of lines in the emission spectrum when photons of energy \(12.75 \mathrm{eV}\) pass through hydrogen gas in the ground state is 6 (Option A).

Step by step solution

01

Convert the energy to joules

To proceed with this exercise, we need to convert the energy of photons from electron volts (eV) to joules (J). We can do this using the conversion factor 1 eV = \(1.602 \times 10^{-19}\) J. Given energy, E = 12.75 eV To convert it to Joules, we multiply it with the conversion factor: E = \(12.75 \times 1.602 \times 10^{-19}\) J E 鈮� \(2.043 \times 10^{-18}\) J
02

Identify the highest energy level

The energy for transitions in a hydrogen atom can be found using the formula: E = \(\frac{(2.18 \times 10^{-18} J)(1 - \frac{1}{n^{2}})}{1 - \frac{1}{(n+1)^{2}}}\) Where E is the energy required for the transition, and n is the energy level of the atom. Now, we need to find the maximum value of n for which the energy E is sufficient. Since the energy E should be equal or greater than the transition energy for hydrogen, we can write the inequality: \(2.043 \times 10^{-18} J\) 鈮� \(\frac{(2.18 \times 10^{-18} J)(1 - \frac{1}{n^{2}})}{1 - \frac{1}{(n+1)^{2}}}\) After solving the inequality, we find that the maximum value of n is 4.
03

Calculate the number of lines in the emission spectrum

To find the number of lines in the emission spectrum when the hydrogen atom transitions from the highest energy level (n=4) to the ground state (n=1), we can use the formula: Number of lines = \(\frac{n(n-1)}{2}\) Where n is the highest energy level. Number of lines = \(\frac{4(4-1)}{2}\) Number of lines = \(\frac{4\times 3}{2}\) Number of lines = \(6\) So, the correct answer is: (A) 6

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The speed of an electron having a wavelength of the order of \(1 \AA\) will be (A) \(7.25 \times 10^{6} \mathrm{~m} / \mathrm{s}\) (B) \(6.26 \times 10^{6} \mathrm{~m} / \mathrm{s}\) (C) \(5.25 \times 10^{6} \mathrm{~m} / \mathrm{s}\) (D) \(4.24 \times 10^{6} \mathrm{~m} / \mathrm{s}\)

Which of the following is a correct statement? (A) Beta rays are same as cathode rays. (B) Gamma rays are high energy neutrons. (C) Alpha particles are double ionized helium atoms. (D) Protons and neutrons have exactly the same mass.

This question contains Statement 1 and statement \(2 .\) Of the four choices given after the statements, choose the one that best describes the two statements. [2008] Statement 1: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and Statement 2: For heavy nuclei, binding energy per nucleon increases with increasing \(Z\) while for light nuclei it decreases with increasing \(Z\). (A) Statement 1 is true, Statement 2 is false (B) Statement 1 is false, Statement 2 is true (C) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for statement 1 (D) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1

Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4 . Then the number of spectral lines in the emission spectra will be: (A) 2 (B) 3 (C) 5 (D) 6

An electromagnetic wave going through vacuum is described by \(E=E_{0} \sin (k x-\omega t) ; B=B_{0} \sin (k x-\omega t)\) Which of the following equation is true? (A) \(E_{0} k=B_{0} \omega\) (B) \(E_{0} \omega=B_{0} k\) (C) \(E_{0} k_{0}=\omega k\) (D) None of these
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Magnetism

Read Explanation

Solid State Physics

Read Explanation

Force

Read Explanation

Thermodynamics

Read Explanation

Work Energy and Power

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.