Validating the Bohr's Model

Q. According to de-Broglie, the de-Broglie wavelength for electron in an orbit of hydrogen atom is ${10}^{–9}\text{m}$. The principle quantum number for this electron is

1. $2$
2. $3$
3. $1$
4. $4$

Q.

A star that is emitting radiation at a wavelength of $5000\mathrm{A}$, is approaching the earth with a velocity of $1.5\times {10}^4\mathrm{m}/\mathrm{s}$. The change in wavelength of the radiation as received on the earth.

Q. The first allowed excited state of a hydrogen atom is 10.2 eV above its lowest energy (ground) state. To what temperature should hydrogen gas be raised so that inelastic collisions may excite an appreciable number of atoms to their first excited state.

1. 
2. 
3. 
4. 

Q.

A particle of mass m moves in a circular orbit in a central potential field $U\left(r\right)=U_0{r}^4$. If Bohr’s quantization conditions are applied, radii of possible orbital $r_n$ vary with $n^{\frac{1}{\alpha }}$, where $\alpha$ is _____ .

Q. The ground state energy of hydrogen atom is -13.6 eV. If an electron makes a transition from an energy level -1.51 eV to -3.4 eV, calculate the wavelength of the spectral line emitted and name the series of hydrogen spectrum to which it belongs.

Q.

The radius of hydrogen atom in the ground state is $5.3\times {10}^{-11}\mathrm{m}$. After collision with an electron it is found to have a radius of $21.2\times {10}^{-11}\mathrm{m}$. The principal quantum number of the final state of the atom is

1. $2$

2. $3$

3. $4$

4. $5$

Q. Why does oil spread over the surface of water but water does not spread over the surface of oil?

Q.

A hydrogen atom emits ultraviolet radition of wavelen gth 102.5 nm. What are the quantum numbers of the states involved in the transition ?

Q. Suppose an electron is attracted towards the originby a force $\frac{k}{r}$ where 'k' is a constant and 'r' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $n^{th}$ orbital of the electrons is found to be '$r_n$' and the kinetic energy of the electron to be '$T_n$'. Then which of the following is true?

1. $T_n\propto \frac{1}{n^2},r_n\propto n^2$
2. $T_n$ independent of n, $r_n\propto n$
3. $T_n\propto \frac{1}{n},r_n\propto n$
4. $T_n\propto \frac{1}{n},r_n\propto n^2$

Q.

The first member of the Balmer series of the Hydrogen atom has a wavelength of $6561\mathrm{\AA }$. The wavelength of the second member of the Balmer series (in nm) is

Q. In terms of potential difference $V$, electric current $I$, permittivity ${\epsilon }_0$, permeability ${\mu }_0$ and speed of light $c$, the dimensionally correct equation(s) is/are

1. ${\mu }_0{I}^2={\epsilon }_0{V}^2$
   
2. ${\epsilon }_{0}I={\mu }_{0}V$
   
   
3. $I={\epsilon }_{0}cV$
   
4. ${\mu }_{0}cI={\epsilon }_{0}V$

Q. Consider a hydrogen atom with its electron in the $n^{th}$ orbital. An electromagnetic radiation of wavelength $90nm$ is used to ionize the atom. If the kinetic energy of the ejected electron is $10.4eV$, then the value of $n$ is ($hc=1242eVnm$)

Q. The radius of the orbit of an electron in a Hydrogen-like atom is $4.5a_0,$ where $a_0$ is the Bohr radius. Its orbital angular momentum is . It is given that $h$ is Planck constant and $R$ is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)

1. $\frac{9}{16R}$
2. $\frac{9}{5R}$
3. $\frac{4}{3R}$
4. $\frac{9}{32R}$

Q. The de broglie wavelength λ associated with a proton increases by 25% if its momentum is deceased by pthe initial momentum was

Q. An electron in an excited state of $L{i}^{2+}$ ion has angular momentum $\frac{3h}{2\pi }$. The de Broglie wavelength of the electron in this state in $p\pi {\alpha }_0$ (where ${\alpha }_0$ is the Bohr radius). The value of $p$ is

Q. What should be the velocity of an electronso that its momentum becomes equal to that of a photon of wavelength 5200 ang

Q. The de-Broglie wavelength of an electron is the same as that of a 50 keV X-ray photon.The ratio of the energy of the photon to the kinetic energy of the electron is (the energy equivalent of electron mass of 0.5MeV)

Q. kinetic energy of an electron which is associated with de-Broglies wavelength 20 angstrom is-1)1.0eV, 2)1.51eV, 3)0.59eV, 4)0.38eV.

Q. If a hydrogen atom in its ground state is excited by means of monochromatic radiation of wavelength $975\mathring{A}$, the number of different lines possible in the resulting spectrum and the longest wavelength among them are

1. $6,18270\mathring{A}$
2. $4,18720\mathring{A}$
3. $4,304\mathring{A}$
4. $6,8208\mathring{A}$

Q.

The electrons revolve only in the orbit in which

1. $\mathrm{mvr}>\frac{\mathrm{nh}}{2\mathrm{\pi }}$

2. $\mathrm{mvr}\ge \frac{\mathrm{nh}}{2\mathrm{\pi }}$

3. $\mathrm{mvr}=\frac{\mathrm{nh}}{2\mathrm{\pi }}$

4. $\mathrm{mvr}<\frac{\mathrm{nh}}{2\mathrm{\pi }}$

Q. Work function of a metal is $2.5\text{eV}$ (Lithium). Which of the following radiations can emit photoelectrons, when incident on its surface.
Radiation Wavelength($\lambda$)
$A$ $2000\mathring{\text{A}}$
$B$ $3000\mathring{\text{A}}$
$C$ $5000\mathring{\text{A}}$
$D$ $6000\mathring{\text{A}}$

1. Only $D$
2. Only $A,B$ and $C$
3. Only $A$ and $B$
4. Only $C$

Q. White light may be considered to be a mixture of wavelengths $\lambda$ ranging between $3900\mathring{A}\text{and}7800\mathring{A}.$ An oil film of thickness $10000\mathring{A}$ is examined normally by reflected light. If $\mu =1.4$ , then the film appears bright for-

1. $4308\mathring{A},5091\mathring{A},6222\mathring{A}$
2. $4000\mathring{A},5091\mathring{A},5600\mathring{A}$
3. $4667\mathring{A},6222\mathring{A},7000\mathring{A}$
4. $4000\mathring{A},4667\mathring{A},5600\mathring{A},7000\mathring{A}$

Q.

Suppose in an imaginary world the angular momentum is quantized to be even intergral multiples of $\frac{h}{2\pi }$. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model ?

Q.

Is Lyman series continuous or not.?

Q.

In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?

1. Singly ionized helium

2. Doubly ionized lithium

3. Hydrogen atom

4. Deuterium atom

Q.

Name the radiations:

whose wavelength range is from $10nm$ to $400nm$.

Q. The first line of the Balmer series in the hydrogen spectrum has a wavelength of $6564\mathring{A}$. Calculate the wavelength of the first line of Lyman series in the same spectrum.

1. $1215\mathring{A}$
2. $1222\mathring{A}$
3. $1346\mathring{A}$
4. $122.5\mathring{A}$

Q. 1--- Suppose the ground state radius and velocity of an electron in a Bohr, s atom are r0 and v0 respectively. If hypothetically the mass of electron becomes 200times of its present value then the ground state radius and velocity will be respectively . 2 --- The ratio of series limit frequencies of Balmer series to that of Bracket series for a H - like atom is .

Q. In Bohr's model of hydrogen atom, the ratio of the period of revolution of an electron in the first orbit to that in the second orbit, is,

1. $1:2$
2. $2:1$
3. $1:4$
4. $1:8$

Q. Write the relation in radius $R$ and mass number $A$ of a nucleus.