IIT JEE and NEET Physics @ Venkats Academy

Showing posts with label Wave Length. Show all posts

Problems and Solutions on Bohr's Atomic Model

Problem and solution

When the electron in hydrogen atom jumps from second orbit to first orbit, a certain wavelength is emitted. When the electron jumps from the third orbit to first orbit, what is the new wavelength emitted in terms of the first wavelength?

We can solve this problem basing on the derivation is that we made for the reciprocal of the wavelength in terms of the Redberg constant. By applying the given condition in the problem in two different equations and by simplifying them we can solve the problem as shown below.

Problem and solution

What is the ratio of largest to shortest wavelengths in the Balmer series of the hydrogen spectrum?

We can solve this problem also basing on the derivation that we made for the reciprocal of the wavelength in terms of principal quantum numbers. For the wavelength to be maximum, the corresponding energy has to be minimum. It is possible only when the electronic jumping from the third orbit to second orbit.

Further wavelength to be minimum, the corresponding energy has to be maximum. This is possible when their electron is jumping from infinite orbit to second orbit. The corresponding equation is written in the problem is solved as shown below.

Problem and solution

In a hydrogen atom electron is jumped from the fifth orbit to first orbit. What is the recoil speed of the hydrogen atom in this process?

As the electronic jumping from higher orbit to lawyer orbit, there is some emission of energy. This emitted energy will have a certain wavelength. To compensate the jerk that is generated by this emitted energy, nuclear is most with a little bit velocity and here we are going to calculate that velocity. By substituting the wavelength that we have derived in the de Broglie concept we can derive the equation for the velocity of the nucleus as shown below.

Problem and solution

If the wavelength of the first member of the Balmer series in the hydrogen spectrum is 6564 Å, what will be the wavelength of the second member of the Balmer series?

We can solve this problem by writing the equation for the reciprocal of the wavelength using the atomic model. By comparing the given two conditions we can get the answer as shown below.

Problem and solution

Related Posts

Dual Nature of Radiation and Matter complete lesson

De Broglie Hypothesis and Wave Nature of Particle

Problems and solutions on de Broglie's Hypothesis

Rutherford Alfa experiment and observations about Atom

Bohr’s atomic model and Radius of Orbit

Velocity and Time period of electron in Bohr orbit

Potential and Kinetic energy of electron in the orbit

Atoms Complete Lesson

De Broglie’s explanation for Bohr’s Angular Momentum

Ray Optics Complete Lesson

Light is a form of energy. It exhibits a wide variety of properties. If the size of the object is much larger than the wavelength of the light, light appears like travelling in straight lines. It exhibits certain properties under these conditions and that properties are studied and rename called Ray optics.

In Ray optics we study about reflection, refraction, dispersion and the deviation.

Reflection is the phenomena of light bouncing back into the same medium after striking a boundary that is separating the two media.

Refraction is the phenomenon of light due to which light travels into the other medium after striking a boundary that is separating the two media.

Dispersion is the phenomenon of splitting up of a white light into multiple colors when it is passed through a prism.

Deviation is the phenomena of changing its path when the light is passing through a different media.

In this chapter we are also going to study regarding mirrors, lenses, prisms, critical angle, total internal reflection, microscopes and telescopes.

This post is a list of all the topics in Ray optics which includes problems and solutions.

Ray Optics Introduction and Reflection of Light

Sign Convention and Image Tracing of Light in Ray Optics

Problems and Solutions on Refraction of Light

Refraction of Light and Snell's Law

Problems and solutions on Refraction of Light

Normal Shift and Lateral Shift due to Refraction of Light

Problems on normal shift Refraction of Light

Critical Angle and Total Internal Reflection

Applications of Total Internal Reflection

Problems and Solutions on Critical angle and Total internal Reflection

Refraction of Light Through Curved Surfaces

Power and Focal Length of a Lens

Refraction of Light Through Prism

Problems and Solutions on Refraction of Light Through Prism

Angular Dispersion and Dispersive Power

Problems on Angular Dispersion and Dispersive Power

Working of Human Eye and Simple Microscope

Working of Compound microscope

Working of a Galilean Telescope

Other Complete Lessons in this blog includes

Units and Dimensions

One and Two Dimensional Motion

Mechanical Properties of Matter

Heat and Thermodynamics

Waves and Oscillations

Wave Optics

Semi Conductor Devices

Dual nature of Radiation and Matter

Stretched String Problems and Solutions

Problem and solution

A sonometer wire has a length of 114 cm between the two fixed ends. Where shall we place two movable bridges to divide the wire into three segments whose fundamental frequency surrender ratio of 1:3:4 ?

When the tension and linear density of the wire is kept constant, frequency of the wire is inversely proportional to its length. Taking this law into consideration the problem is solved as shown below.

Problem and solution

A wire with density and length given and extension under a load is given in the below problem.We need to calculate the frequency of the wire under fundamental mode using the formula for the frequency of a stretched string.

This problem is based on law of tension.When frequency is changed its tension will change as shown below.

Frequency of the tuning fork is directly proportional to thickness of the fork, velocity of the wave and inversely proportional to Squire of its length.

Speed of a longitudinal wave in a medium

The velocity of a wave in a medium can be expressed as the ratio of Squire root of modulus of elasticity of the medium to the density of the medium. It is assumed that the propagation of the sound happens in a isothermal way. Anyway practically it is found that the temperature of the particles of the medium is not going to remain constant during the propagation of the wave. It is rather in adiabatic process when the heat energy of the system remains constant but the temperature increases.

It can be further proved that velocity of sound is independent of pressure.When ever pressure changes its volume also changes which generates same change in density and hence the ratio of pressure to density remain constant.