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Naturally occurring vanadium is composed of one stable isotope, 51 V, and one radioactive isotope, 50 V. The latter has a half-life of 2.71×10 17 years and a natural abundance of 0.25%. 51 V has a nuclear spin of 7 ⁄ 2 , which is useful for NMR spectroscopy . [ 25 ]
Vanadium compounds are compounds formed by the element vanadium (V). The chemistry of vanadium is noteworthy for the accessibility of the four adjacent oxidation states 2–5, whereas the chemistry of the other group 5 elements , niobium and tantalum , are somewhat more limited to the +5 oxidation state. [ 1 ]
The cross product with respect to a right-handed coordinate system. In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol .
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Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge. Thus, an object's charge can be exactly 0 e, or exactly 1 e, −1 e, 2 e, etc., but not 1 / 2 e, or −3.8 e, etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.)
The vanadium redox battery (VRB), also known as the vanadium flow battery (VFB) or vanadium redox flow battery (VRFB), is a type of rechargeable flow battery. It employs vanadium ions as charge carriers . [ 6 ]
Coupled substitution is the geological process by which two elements simultaneous substitute into a crystal in order to maintain overall electrical neutrality and keep the charge constant. [1] In forming a solid solution series, ionic size is more important than ionic charge , as this can be compensated for elsewhere in the structure.
In three dimensions the cross product is invariant under the action of the rotation group, SO(3), so the cross product of x and y after they are rotated is the image of x × y under the rotation. But this invariance is not true in seven dimensions; that is, the cross product is not invariant under the group of rotations in seven dimensions, SO(7).