Lise Meitner and Nuclear Fission

• Lise Meitner, an Austrian theoretical nuclear physicist, introduced the term "nuclear fission".
• Meitner provided the theory behind the splitting of uranium atoms' nuclei, which her colleagues first demonstrated in 1938.

Milestones

• In 1907, Meitner moved to Berlin to work as a departmental assistant at Max Planck's physics institute.
• Meitner was awarded the Leibniz Medal and became the supervisor of the physics section at the University of Berlin in 1917.
• In July 1938, Meitner escaped Nazi Germany and settled in Sweden when Austrian citizens became subject to German law.
• Along with Otto Frisch, Meitner published the theory of nuclear fission in Nature on February 11, 1939.
• In 1966, Meitner, along with Hahn and Strassman, received the Enrico Fermi Award from the US Atomic Energy Commission

Early Life and Education

• Meitner was raised in Vienna as the third of eight children in a liberal Jewish family.
• Her father, Philipp, a lawyer, along with his wife Hedwig, cultivated a stimulating environment.
• Writers, lawyers, legislators, politicians, and chess players were often present at family gatherings.
• At age 8, Meitner kept a mathematics notebook under her pillow and asked probing questions.
• Philipp ensured Meitner was privately tutored when she turned 14, after which girls were barred from state schooling.
• Meitner's private tuition aimed to pass the University of Vienna entrance exam.
• She passed the exam in July 1902 and at 23, became one of the first women to attend the university's physics course.
• Tutored by Ludwig Boltzmann, Meitner became the second woman at the university to earn a physics doctorate in February 1906.
• Her thesis explored how heat travels through inhomogeneous solids and how they conduct heat similarly to electricity.

Later Life

• After fleeing to Sweden, Meitner initially struggled to interpret her nuclear fission experiment's results
• She explained the process of fission using data that Hahn sent by letter

Vector Space Definition

• A vector space E that is supplied with 2 operations:
• Addition: + : E x E -> E
• Multiplication by a scalar K x E -> E
• $Associativity: \forall u, v, w \in E, (u + v) + w = u + (v + w)$
• $Commutativity: \forall u, v \in E, u + v = v + u$
• $Neutral element: \exists 0_E \in E, \forall u \in E, u + 0_E = u$
• $Opposite element: \forall u \in E, \exists -u \in E, u + (-u) = 0_E$
• $Distributivity with respect to vector addition : \forall \lambda \in K, \forall u, v \in E, \lambda(u + v) = \lambda u + \lambda v$
• $Distributivity with respect to scalar addition : \forall \lambda, \mu \in K, \forall u \in E, (\lambda + \mu)u = \lambda u + \mu u$
• $Compatibility of scalar multiplication : \forall \lambda, \mu \in K, \forall u \in E, (\lambda \mu)u = \lambda(\mu u)$
• $Neutral element for scalar multiplication : \forall u \in E, 1_K u = u$

Vector Subspace Definition

• A subset F of a vector space E is a vector subspace if:
• F is non-empty
• $\forall u, v \in F, u + v \in F$
• $\forall \lambda \in K, \forall u \in F, \lambda u \in F$

Linear Combination Definition

• A linear combination of vectors $v_1, v_2,..., v_n$ is a vector of the form:
• $\lambda_1 v_1 + \lambda_2 v_2 +... + \lambda_n v_n$ où $\lambda_i \in K$

Spanning Set Definition

• A family of vectors $(v_1, v_2,..., v_n)$ generates E if every vector of E can be written as a linear combination of these vectors.

Free Family Definition

• A family of vectors $(v_1, v_2,..., v_n)$ is free if:
• $\lambda_1 v_1 + \lambda_2 v_2 +... + \lambda_n v_n = 0_E \implies \lambda_1 = \lambda_2 =... = \lambda_n = 0$

Base Definition

• A basis of E is a family of vectors that is both free and generating.

Dimension Definition

• The dimension of E is the number of vectors in a basis of E.

Linear Applications

• A map $f : E \rightarrow F$ is linear if:
• $\forall u, v \in E, f(u + v) = f(u) + f(v)$
• $\forall \lambda \in K, \forall u \in E, f(\lambda u) = \lambda f(u)$

Kernel Definition

• The kernel of f is the set of vectors of E that are sent to $0_F$ by f.
• $Ker(f) = {u \in E \mid f(u) = 0_F}$

Image Definition

• The image of f is the set of vectors of F that are reached by f.
• $Im(f) = {v \in F \mid \exists u \in E, f(u) = v}$

Rank Theorem

• Let $f : E \rightarrow F$ be a linear application. Then:
• $dim(E) = dim(Ker(f)) + dim(Im(f))$