In a Rutherford scattering experiment when a projectile of charge $z_1$ and mass $M_1$ approaches a target nucleus of charge $z_2$ and mass $M_2$, the distance of closest approach is $r_0$ The energy of the projectile is
In a Rutherford scattering experiment when a projectile of charge $z_1$ and mass $M_1$ approaches a target nucleus of charge $z_2$ and mass $M_2$, the distance of closest approach is $r_0$ The energy of the projectile is
- [AIPMT 2009]
- A
directly proportional to $Z_1 Z_2$
- B
inversely proportional to $Z_1$
- C
directly proportional to $m_1\times m_2 $
- D
directly proportional to mass $m_1 $
Similar Questions
The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about $10^{-40} .$ An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction.
The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about $10^{-40} .$ An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction.
Difference between nth and $(n +1)^{th}$ Bohr’s radius of $‘H’$ atom is equal to it’s $(n-1)^{th}$ Bohr’s radius. the value of $n$ is:
Difference between nth and $(n +1)^{th}$ Bohr’s radius of $‘H’$ atom is equal to it’s $(n-1)^{th}$ Bohr’s radius. the value of $n$ is:
The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number $Z$ of hydrogen like ion is
The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number $Z$ of hydrogen like ion is
Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom $\left(\sim 10^{-10} \;m \right)$
$(a)$ Construct a quantity with the dimensions of length from the fundamental constants $e, m_{e},$ and $c .$ Determine its numerical value.
$(b)$ You will find that the length obtained in $(a)$ is many orders of magnitude smaller than the atomic dimensions. Further, it involves $c .$ But energies of atoms are mostly in non-relativistic domain where $c$ is not expected to play any role. This is what may have suggested Bohr to discard $c$ and look for 'something else' to get the right atomic size. Now, the Planck's constant $h$ had already made its appearance elsewhere. Bohr's great insight lay in recognising that $h, m_{e},$ and $e$ will yield the right atomic size. Construct a quantity with the dimension of length from $h m_e$, and $e$ and confirm that its numerical value has indeed the correct order of magnitude.
Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom $\left(\sim 10^{-10} \;m \right)$
$(a)$ Construct a quantity with the dimensions of length from the fundamental constants $e, m_{e},$ and $c .$ Determine its numerical value.
$(b)$ You will find that the length obtained in $(a)$ is many orders of magnitude smaller than the atomic dimensions. Further, it involves $c .$ But energies of atoms are mostly in non-relativistic domain where $c$ is not expected to play any role. This is what may have suggested Bohr to discard $c$ and look for 'something else' to get the right atomic size. Now, the Planck's constant $h$ had already made its appearance elsewhere. Bohr's great insight lay in recognising that $h, m_{e},$ and $e$ will yield the right atomic size. Construct a quantity with the dimension of length from $h m_e$, and $e$ and confirm that its numerical value has indeed the correct order of magnitude.
Consider the following statements:
$I$. All isotopes of an element have the same number of neutrons.
$II$. Only one isotope of an element can be stable and non-radioactive.
$III$. All elements have isotopes.
$IV$. All isotopes of carbon can form chemical compounds with oxygen-$16$.
Choose the correct option regarding an isotope.
Consider the following statements:
$I$. All isotopes of an element have the same number of neutrons.
$II$. Only one isotope of an element can be stable and non-radioactive.
$III$. All elements have isotopes.
$IV$. All isotopes of carbon can form chemical compounds with oxygen-$16$.
Choose the correct option regarding an isotope.
- [KVPY 2014]