MCQ
The $log-log$ graph between the energy $E$ of an electron and its de-Broglie wavelength $\lambda $ will be
- A
- B
- ✓
- D
✓
Answer
Correct option: C.
c
(c) $\lambda = \frac{h}{{\sqrt {2mE} }} = \frac{h}{{\sqrt {2m} }} \cdot \frac{1}{{\sqrt E }}$.
(c) $\lambda = \frac{h}{{\sqrt {2mE} }} = \frac{h}{{\sqrt {2m} }} \cdot \frac{1}{{\sqrt E }}$.
Taking $log$ of both sides $\log \lambda = \log \frac{h}{{\sqrt 2 m}} + \log \frac{1}{{\sqrt E }}$
$⇒$ $\log \lambda = \log \frac{h}{{\sqrt 2 m}} - \frac{1}{2}\log E$
$ \Rightarrow \log \lambda = - \frac{1}{2}\log E + \log \frac{h}{{\sqrt {2m} }}$
This is the equation of straight line having slope $(-1/2)$ and positive intercept on log $\lambda$axis.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
An $e^-$ is moving parallel to a long current carrying wire as shown. Force on electron is
→A transverse harmonic wave on a string is given by $y(x, t)=5 \sin (6 t+0.003 x)$ where $x$ and $y$ are in $cm$ and $t$ in $sec$. The wave velocity is $...........\,ms ^{-1}$.
→Two electric bulbs rated ${P_1}\,watt$ $V\, volts$ and ${P_2}\, watt$ $V\, volts$ are connected in parallel and $V\, volts$ are applied to it. The total power will be
→Two bodies of masses $2\,kg$ and $4\,kg$ are moving with velocities $2\,m/s$ and $10\,m/s$ respectively towards each other due to mutual gravitational attraction. ....... $m/s$ is the velocity of their centre of mass (Bodies are at rest initially)
→A black body is at a temperature of $500 \;K$, it emits energy at a rate which is proportional to
→The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant, its length must be increased by ..... $\%$
→If the critical angle for total internal reflection from a medium to vacuum is $30^o $, the velocity of light in the medium is
→$X$ different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number ${n}=6$ ? The value of ${X}$ is ..... .
→$A$ object is placed at a distance of $15\,cm$ from a convex lens of focal length $10\,cm$. On the other side of the lens, a convex mirror is placed at its focus such that the image formed by the combination coincides with the object itself. The focal length of the convex mirror is.....$cm$
→A copper disc of radius $0.1\, m$ rotates about its centre with $10$ revolutions per second in a uniform magnetic field of $0.1$ Tesla. The emf induced across the radius of the disc is
→